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.expand_btn{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .cwITDy .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .cwITDy ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .cwITDy ol li{margin:10px 0;padding-left:10px;word-break:normal;} .cwITDy ol li a{word-break:break-all;} .cwITDy ol li .reflinks{display:block;} .cwITDy ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .cwITDy ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .cwITDy ol li .reflinks .sep{color:#000000;} .cwITDy .table-wrapper{width:auto;overflow-x:auto;} .cwITDy .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .cwITDy .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.cwITDy .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.cwITDy .table-wrapper{width:auto;}} @media (min-width:1324px){.cwITDy .table-wrapper{width:auto;}} @media (min-width:320px){.cwITDy{margin-bottom:33px;padding:0;}} @media (min-width:992px){.cwITDy{padding:0;margin-bottom:100px;}} @media (min-width:1325px){.cwITDy{margin-bottom:100px;}} .cwITDy .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .cwITDy .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .cwITDy .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;} .cwITDy .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .cwITDy .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .cwITDy 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href="//www.newsama.com/journals/jps/" aria-label="Journal of Probability and Statistics">概率论与数理统计》杂志上</gydF4y2Baa>/<gydF4y2Baa class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jps/contents/year/2012/" aria-label="2012">2012年</gydF4y2Baa>/<gydF4y2Baspan class="sc-bhlBdH UVThf">文章</gydF4y2Baspan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</p><gydF4y2Baspan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#abstract" aria-label="">文摘</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#introduction" aria-label="">介绍</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#discussion" aria-label="">讨论</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#acknowledgments" aria-label="">确认</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#references" aria-label="">引用</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#related-articles" aria-label="">相关文章</gydF4y2Baa></span> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <div class="sc-kxynE fgGykB"> <span class="sc-cooIXK gQxyld">特殊的问题</gydF4y2Baspan> <h2 class="sc-fcdeBU bVtmCk">联合模型及其应用</gydF4y2Bah2> <a class="sc-htpNat bUhGXt link sc-gmeYpB hSHJbi" href="//www.newsama.com/journals/jps/si/735909/" aria-label="">把这个特殊的问题</gydF4y2Baa> <hr class="sc-clNaTc ktFfKO"> </div> <p class="sc-kZmsYB bkiEfx article_type">评论文章|<gydF4y2Ba!-- -->开放获取</p><gydF4y2Badiv class="sc-RcBXQ ztvYg article_citation"> 体积<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</gydF4y2Baspan>文章的ID<gydF4y2Ba!-- --> 640153年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</gydF4y2Baspan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2012/640153" aria-label="Doi-link">https://doi.org/10.1155/2012/640153</gydF4y2Baa> </div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>朗吴、刘魏、优雅y,黄养心<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<gydF4y2Baspan class="adjust-article-svg-size">纵向和生存分析数据:联合建模、推理方法和问题</gydF4y2Baspan>”,<gydF4y2Ba!-- --><i>概率论与数理统计》杂志上</我>,<ggydF4y2BaydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2012年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->640153年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 17<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2012/640153</p></gydF4y2Badiv> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN dULHFk article_title adjust-article-svg-size heading-title">纵向和生存分析数据:联合建模、推理方法和问题</gydF4y2Bah1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>朗吴</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<gydF4y2Basup>1</gydF4y2Basup></span> <span class="">刘魏<gydF4y2Ba!-- -->,<gydF4y2Basup>2</gydF4y2Basup></span> <span class="">恩典y易<gydF4y2Ba!-- -->,<gydF4y2Basup>3</gydF4y2Basup> 和</gydF4y2Baspan> <span class="">养心黄<gydF4y2Basup>4</gydF4y2Basup></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</gydF4y2Basup><span>部门统计,不列颠哥伦比亚大学,温哥华BC,加拿大</gydF4y2Baspan></p> <p><sup>2</gydF4y2Basup><span>数学和统计,约克大学,多伦多,加拿大</gydF4y2Baspan></p> <p><sup>3</gydF4y2Basup><span>部门统计和精算,滑铁卢大学,滑铁卢,加拿大</gydF4y2Baspan></p> <p><sup>4</gydF4y2Basup><span>流行病学和生物统计学、公共卫生学院,南佛罗里达大学,坦帕,高度层33612,美国</gydF4y2Baspan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>Wenbin陆</gydF4y2Badiv> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年8月25日</gydF4y2Baspan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年10月10日</gydF4y2Baspan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年12月07</gydF4y2Baspan> </div> </div> </div> <article class="sc-jtRlXQ cwITDy article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>在过去的二十年里,联合模型的纵向和生存数据文献中得到太多的关注。这些模型往往是可取的下列情形:(i)生存模型与测量错误或缺失的数据时间,(2)纵向模型用有用的辍学者,和(3)生存的过程和一个纵向的过程通过潜变量相关联。在这些情况下,单独的推论基于纵向模型和生存模型可能导致偏见或效率低下的结果。在这篇文章中,我们提供一个简要的概述纵向和生存数据的联合模型和常用的方法,包括方法和可能性两阶段方法。</p><gydF4y2Baspan class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>纵向数据和生存在实践中经常出现在一起。例如,在许多医学研究,我们经常收集病人的信息(例如,血压)不断随着时间的推移,我们也感兴趣的恢复时间或复发的疾病。纵向数据和生存数据往往<我>相关的</我>在某些方面。时间事件可能与纵向轨迹有关。<我>单独的</我>分析纵向数据和生存数据可能导致效率低下或有偏见的结果。纵向和生存数据的联合模型,另一方面,同时将所有信息,并提供有效的和有效的推论。</p><p>gydF4y2Ba图<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/fig1/" target="_blank">1</gydF4y2Baa>显示了一个纵向数据集的CD4细胞计数测量不断随着时间的推移,在艾滋病的研究。在这里,时间事件可以时间到病毒反弹,辍学,或时间,根据研究目标。数据分析主要集中在纵向数据或生存数据或两者兼而有之。集中在纵向数据分析时,我们经常需要解决的辍学因为辍学是很常见的纵向研究。关注生存数据分析时,我们常常需要把时间如CD4反是因为次事件可能与协变量相关联的轨迹。有时,主要兴趣可能在于纵向过程和生存之间的关系的过程。在这些情况下,联合模型特性相关的纵向和生存所需的数据。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="(一)”name="640153.fig.001a" src="https://static-01.hindawi.com/articles/jps/volume-2012/640153/figures/640153.fig.001a.jpg"> <br> <strong>(一)</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”name="640153.fig.001b" src="https://static-01.hindawi.com/articles/jps/volume-2012/640153/figures/640153.fig.001b.jpg"> <br> <strong>(b)</gydF4y2Bastrong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig1"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”name="640153.fig.001a" src="https://static-01.hindawi.com/articles/jps/volume-2012/640153/figures/640153.fig.001a.jpg"><br><strong>(一)</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”name="640153.fig.001b" src="https://static-01.hindawi.com/articles/jps/volume-2012/640153/figures/640153.fig.001b.jpg"><br><strong>(b)</gydF4y2Bastrong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig1"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2012/640153/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 随着时间的推移CD4测量。(一)所有科目。(b)五个随机选择的科目。</gydF4y2Batable> </div> </div> </div> <p>通常情况下,联合模型纵向和生存数据需要在以下情况下:<gydF4y2Baspan class="list"><span class="list-item"><span class="list-label">(我)</gydF4y2Baspan><span class="list-content">生存模型协变量与时间测量误差;</gydF4y2Baspan></span><span class="list-item"><span class="list-label">(2)</gydF4y2Baspan><span class="list-content">纵向模型用有用的辍学;</gydF4y2Baspan></span><span class="list-item"><span class="list-label">(3)</gydF4y2Baspan><span class="list-content">纵向和生存过程是由一个共同的潜在过程;</gydF4y2Baspan></span><span class="list-item"><span class="list-label">(iv)</gydF4y2Baspan><span class="list-content">外部信息的使用更高效的推理。</gydF4y2Baspan></span></span></p> <p>联合模型的纵向和生存数据吸引了越来越多的关注在过去的二十年。Tsiatis和Davidian<gydF4y2Baa href="#B23">1</gydF4y2Baa>)提供了一个不错的早期工作联合模型的概述,包括德Gruttola和你<gydF4y2Baa href="#B2">2</gydF4y2Baa>],Wulfsohn和Tsiatis [<gydF4y2Baa href="#B29">3</gydF4y2Baa>),亨德森et al。<gydF4y2Baa href="#B7">4</gydF4y2Baa>王,和泰勒(<gydF4y2Baa href="#B24">5</gydF4y2Baa>),等等。最近的工作包括丁和王<gydF4y2Baa href="#B3">6</gydF4y2Baa>),Nathoo和院长<gydF4y2Baa href="#B16">7</gydF4y2Baa>),你们et al。<gydF4y2Baa href="#B31">8</gydF4y2Baa>],艾伯特和施<gydF4y2Baa href="#B1">9</gydF4y2Baa>),Jacqmin-Gadda et al。<gydF4y2Baa href="#B11">10</gydF4y2Baa>),Rizopoulos et al。<gydF4y2Baa href="#B19">11</gydF4y2Baa>),吴et al。<gydF4y2Baa href="#B28">12</gydF4y2Baa>),黄等。<gydF4y2Baa href="#B9">13</gydF4y2Baa>),锅和彝语(<gydF4y2Baa href="#B17">14</gydF4y2Baa>),等等。一个典型的模型设置假设mixed-effects模型的纵向数据和Cox模型或加速故障时间(尾部)模型生存数据,与两个模型共享一些随机效应或变量。可能性的方法是经常使用,通过EM算法实现。另一个常见的方法是基于两阶段方法,计算简单。亨德森et al。<gydF4y2Baa href="#B7">4</gydF4y2Baa>)允许不同纵向和生存的随机效应模型,但假设随机效应相关。贝叶斯方法也被提出(<gydF4y2Baa href="#B9">13</gydF4y2Baa>,<gydF4y2Baa href="#B30">15</gydF4y2Baa>,<gydF4y2Baa href="#B10">16</gydF4y2Baa>]。</p><p>gydF4y2Ba自文献联合模型相当广泛,很难评估的所有引用。在本文中,我们提供了一个简短回顾联合模型的文献。节<gydF4y2Baa href="#sec2">2</gydF4y2Baa>我们描述一个标准制定联合模型。节<gydF4y2Baa href="#sec3">3</gydF4y2Baa>,我们回顾一个常用的两阶段法。节<gydF4y2Baa href="#sec4">4</gydF4y2Baa>,我们描述标准的可能性的方法。节<gydF4y2Baa href="#sec5">5</gydF4y2Baa>,我们将讨论一些标准的联合模型的扩展。一个真实数据的例子和仿真研究提出了在部分<gydF4y2Baa href="#sec6">6</gydF4y2Baa>为了说明和评价方法。我们在部分总结本文<gydF4y2Baa href="#sec7">7</gydF4y2Baa>与讨论。</p><gydF4y2Bah4 id="a-standard-formulation-of-a-joint-model">2。一个标准的制定的联合模型</gydF4y2Bah4> <p>在本节中,我们考虑一个标准制定的联合模型。在文献中,一个典型的设置是一个生存模型与测量误差在时间,在一个线性mixed-effects (LME)协变量模型通常用于模型时间解决协变量测量误差和Cox比例风险(PH)模型用于建模的生存数据。我们关注这个设置说明的基本观念。</p><p>gydF4y2Ba考虑一个纵向研究<gydF4y2Basvg height="7.1374998" id="M1" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>个人在示例。目标是模型感兴趣的时间一个事件或生存时间。变化在生存模型用于部分解释事件的变化。让<gydF4y2Basvg height="11.05" id="M2" style="vertical-align:-3.2316pt;width:11.025px;" version="1.1" viewbox="0 0 11.025 11.05" width="11.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>个人的生存时间<gydF4y2Basvg height="9.9250002" id="M3" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="12.8875" id="M4" style="vertical-align:-1.76814pt;width:85.537498px;" version="1.1" viewbox="0 0 85.537498 12.8875" width="85.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.108906" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.901154" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.114902" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。一些人可能不会经历任何事件的研究他们的活动时间<我>正确的审查</我>。我们假设随机或审查<我>non我nformative</我>。对个人<gydF4y2Basvg height="9.9250002" id="M5" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="11.05" id="M6" style="vertical-align:-3.2316pt;width:10.6375px;" version="1.1" viewbox="0 0 10.6375 11.05" width="10.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>审查时间,让<gydF4y2Basvg height="14.7125" id="M7" style="vertical-align:-3.2316pt;width:89.487503px;" version="1.1" viewbox="0 0 89.487503 14.7125" width="89.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.16,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.76,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.07,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样的审查指标<gydF4y2Basvg height="14.7125" id="M8" style="vertical-align:-3.2316pt;width:38.587502px;" version="1.1" viewbox="0 0 38.587502 14.7125" width="38.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.16,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>如果个人的生存时间<gydF4y2Basvg height="9.9250002" id="M9" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是正确的审查,<gydF4y2Basvg height="14.7125" id="M10" style="vertical-align:-3.2316pt;width:38.587502px;" version="1.1" viewbox="0 0 38.587502 14.7125" width="38.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.16,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>否则。观察到的生存数据<gydF4y2Basvg height="14.775" id="M11" style="vertical-align:-3.2316pt;width:149.3625px;" version="1.1" viewbox="0 0 149.3625 14.775" width="149.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.164939" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.87,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-54.65,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.65,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.43,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.528246" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.932903" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.184402" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.385651" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.63715" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.850903" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.441902" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.64315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.85714" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="14.825" id="M12" style="vertical-align:-3.2316pt;width:96.287498px;" version="1.1" viewbox="0 0 96.287498 14.825" width="96.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.34,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> n</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.809551" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.02,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.8,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-2.4,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.82,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</p><p>gydF4y2Ba在生存模型,一些时间不可能测量错误。为简单起见,我们考虑一个时间协变量。让<gydF4y2Basvg height="13.1125" id="M13" style="vertical-align:-4.77652pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 13.1125" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1125)"> <g transform="translate(72,-61.51)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<我>观察到的</我>协变量值对个人<gydF4y2Basvg height="9.9250002" id="M14" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在时间<gydF4y2Basvg height="12.975" id="M15" style="vertical-align:-4.77652pt;width:16.475px;" version="1.1" viewbox="0 0 16.475 12.975" width="16.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.02,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>受测量误差,<gydF4y2Basvg height="12.8875" id="M16" style="vertical-align:-1.76814pt;width:85.537498px;" version="1.1" viewbox="0 0 85.537498 12.8875" width="85.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.108906" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.901154" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.114902" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>;<gydF4y2Basvg height="14.7125" id="M17" style="vertical-align:-3.2316pt;width:94.112503px;" version="1.1" viewbox="0 0 94.112503 14.7125" width="94.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.832638" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.084137" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.285385" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.876389" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.090137" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.02,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让相应的未被注意的<我>真正的</我>协变量的值是<gydF4y2Basvg height="18.1875" id="M18" style="vertical-align:-5.34312pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 18.1875" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1875)"> <g transform="translate(72,-57.45)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="8.6899996"> </gydF4y2Batspan> </text> </g> </g> </svg>。表示<gydF4y2Basvg height="20.4625" id="M19" style="vertical-align:-5.39853pt;width:120.475px;" version="1.1" viewbox="0 0 120.475 20.4625" width="120.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4625)"> <g transform="translate(72,-55.63)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.71,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-37.27,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.67,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,1.58,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,10.51,55.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,13.45,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,17.62,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="21.1625" id="M20" style="vertical-align:-5.96513pt;width:123.1px;" version="1.1" viewbox="0 0 123.1 21.1625" width="123.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.1625)"> <g transform="translate(72,-55.07)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.15,66.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.6,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.16,66.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="9.2200003"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-27.56,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,3.68,66.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,12.62,55.19)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,15.56,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.72,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。在许多情况下,纵向协变量的测量在事件或终止审查时间<gydF4y2Basvg height="13.0125" id="M21" style="vertical-align:-3.2316pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 13.0125" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。例如,事件是辍学时是这样。在这种情况下,我们有<gydF4y2Basvg height="16.375" id="M22" style="vertical-align:-5.39853pt;width:50.6875px;" version="1.1" viewbox="0 0 50.6875 16.375" width="50.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.02,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.09,59.02)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-50.67,64.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.72,61.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>事件时间后,协变量的值<gydF4y2Basvg height="13.0125" id="M23" style="vertical-align:-3.2316pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 13.0125" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>都是缺失的。让<gydF4y2Basvg height="11.3625" id="M24" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.3625" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>协变量是没有测量误差。</p><p>gydF4y2Ba我们考虑以下Cox模型生存数据:<gydF4y2Baspan class="equation" id="EEq1"> <svg height="19.35" id="M25" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,79.46,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,86.23,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,91.53,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.04,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133,61.14)"> <tspan style="font-size: 12.50px; " x="36.549999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.400002" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.867268" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.118767" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.64,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.8,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.29,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,216.94,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.79,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25999999" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.5,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,249.31,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.19,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.09614" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.460405" y="-2.51"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.500793" y="-2.51"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.752296" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.953545" y="-2.51"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.54454" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.758293" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.972282" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="210.56" y="-2.51"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="214.7235" y="-2.51"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.97501" y="-2.51"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.10075" y="-2.51"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="230.35225" y="-2.51"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="14.7125" id="M26" style="vertical-align:-3.2316pt;width:27.9px;" version="1.1" viewbox="0 0 27.9 14.7125" width="27.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.97,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是风险函数,<gydF4y2Basvg height="14.75" id="M27" style="vertical-align:-3.25793pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 14.75" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>未指明的基线风险函数,<gydF4y2Basvg height="18.7875" id="M28" style="vertical-align:-3.94627pt;width:91.762497px;" version="1.1" viewbox="0 0 91.762497 18.7875" width="91.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7875)"> <g transform="translate(72,-56.97)"> <text transform="matrix(1,0,0,-1,-71.95,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.453708" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.481594" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.645094" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.13,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.26,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.23,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.52,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-5.36,66.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是未知参数。生存模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)假设风险函数<gydF4y2Basvg height="14.7125" id="M29" style="vertical-align:-3.2316pt;width:27.9px;" version="1.1" viewbox="0 0 27.9 14.7125" width="27.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.97,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>取决于<我>未被注意的真实</我>协变量的值<gydF4y2Basvg height="16.262501" id="M30" style="vertical-align:-3.7982pt;width:29.5625px;" version="1.1" viewbox="0 0 29.5625 16.262501" width="29.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.64,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,而不是观察到但量错协变量的值<gydF4y2Basvg height="14.7125" id="M31" style="vertical-align:-3.2316pt;width:27.25px;" version="1.1" viewbox="0 0 27.25 14.7125" width="27.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.49,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</p><p>gydF4y2Ba在考克斯模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>),含协变量的值<gydF4y2Basvg height="14.7125" id="M32" style="vertical-align:-3.2316pt;width:27.25px;" version="1.1" viewbox="0 0 27.25 14.7125" width="27.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.49,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>应该可以在任何情况下时间吗<gydF4y2Basvg height="9.125" id="M33" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。然而在实践中,反是通常测量<我>断断续续</我>有时(说)<gydF4y2Basvg height="16.700001" id="M34" style="vertical-align:-4.77652pt;width:137.1875px;" version="1.1" viewbox="0 0 137.1875 16.700001" width="137.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.02,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-52.87,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.704248" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.209888" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.461388" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.662636" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.253639" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.467384" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,28.48,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,31.7,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>对个人<gydF4y2Basvg height="9.9250002" id="M35" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在个人,测量时间可能不同,可能导致“失踪的协变量。“此外,反是可以测量错误。因此,它都是很常见的<我>缺失的数据</我>和<我>测量错误</我>协变量在时间,必须解决进行推理时基于Cox模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)。为简单起见,我们假设随机丢失的协变量数据丢失(<gydF4y2Baa href="#B14">17</gydF4y2Baa>]。</p><p>gydF4y2Ba处理缺失数据或测量误差或两个,一个标准的方法是模型协变量的时间。一个共同的选择是以下LME模型:<gydF4y2Baspan class="equation" id="EEq2"> <svg height="16.262501" id="M36" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,94.43,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.98,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,106.68,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.53,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,130.75,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.417879" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.36,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.58,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,169.83,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.83,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.69,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,200.38,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.22,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.07,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,243.93,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.15,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.530407" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.570793" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.822296" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.023544" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.614544" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.828293" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.04229" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="217.60001" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="221.7635" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="228.015" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="231.14075" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="237.39224" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="14.3625" id="M37" style="vertical-align:-3.2316pt;width:15.1625px;" version="1.1" viewbox="0 0 15.1625 14.3625" width="15.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.14,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.3625" id="M38" style="vertical-align:-3.2316pt;width:13.1375px;" version="1.1" viewbox="0 0 13.1375 14.3625" width="13.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.76,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是已知的设计矩阵,<gydF4y2Basvg height="7.5124998" id="M39" style="vertical-align:-0.15048pt;width:10.5px;" version="1.1" viewbox="0 0 10.5 7.5124998" width="10.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.5125)"> <g transform="translate(72,-65.99)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是固定后果的向量参数,<gydF4y2Basvg height="11.55" id="M40" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个向量随机效应,<gydF4y2Basvg height="20.4625" id="M41" style="vertical-align:-5.39853pt;width:119.525px;" version="1.1" viewbox="0 0 119.525 20.4625" width="119.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4625)"> <g transform="translate(72,-55.63)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.44,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-58.74,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-37.17,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.57,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.81,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.75,55.75)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,12.69,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,16.85,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个矢量的测量误差,无法真正的则反是<gydF4y2Basvg height="16.262501" id="M42" style="vertical-align:-3.7982pt;width:101.0375px;" version="1.1" viewbox="0 0 101.0375 16.262501" width="101.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.15,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.6,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.75,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.53,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.077658" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.417879" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.91,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.69,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.56,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。通常,我们假设<gydF4y2Baspan class="equation" id="eq1"> <svg height="19.475" id="M43" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,117.57,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,123.82,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,130.51,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.88121" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.044708" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.296207" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.50996" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.474609" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.726112" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.85714" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.89,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,225.58,61.03)"> <tspan style="font-size: 12.50px; " x="25.889999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.74" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.991501" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.192749" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.12,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.99,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.1300001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.07" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.75999" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.92349" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.175" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.30075" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="203.55225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>和<gydF4y2Basvg height="11.55" id="M44" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="11.3625" id="M45" style="vertical-align:-3.2316pt;width:12.2875px;" version="1.1" viewbox="0 0 12.2875 11.3625" width="12.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.44,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是独立的,<gydF4y2Basvg height="10.55" id="M46" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>协方差矩阵,<gydF4y2Basvg height="13.9375" id="M47" style="vertical-align:-0.13794pt;width:15.3875px;" version="1.1" viewbox="0 0 15.3875 13.9375" width="15.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9375)"> <g transform="translate(72,-60.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>是一个参数,<gydF4y2Basvg height="10.325" id="M48" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个单位矩阵。在这里,我们专注于协变量的情况下,观测过程被截断的事件;后,没有协变量的数据是可用的事件发生时(如死亡或辍学)。</p><p>gydF4y2Ba注意,生存模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)和纵向模型(<gydF4y2Baa href="#EEq2">2.2</gydF4y2Baa>)<我>通过共享随机效应有关</我><svg height="11.55" id="M49" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。在某些应用程序中,不一定在测量误差情况下,共享的随机效应可能被视为一个潜在的过程管理纵向过程和生存过程。共享随机效应引起的<我>依赖</我>纵向和生存之间的流程,这种依赖表明联合建模的需要。</p><p>gydF4y2Ba有两种常用的推理方法的联合模型:<gydF4y2Baspan class="list"><span class="list-item"><span class="list-label">(我)</gydF4y2Baspan><span class="list-content">两阶段方法,</gydF4y2Baspan></span><span class="list-item"><span class="list-label">(2)</gydF4y2Baspan><span class="list-content">可能性的方法。</gydF4y2Baspan></span></span></p> <p>在下面几节中,我们详细描述这两种方法。其他方法联合模式也被提出,如那些基于估计方程,但是我们忽略了空间的考虑。</p><gydF4y2Bah4 id="two-stage-methods">3所示。两阶段方法</gydF4y2Bah4> <p>联合建模文学、各种两阶段方法。一个简单的(天真)两阶段方法如下。</p><p><gydF4y2Baspan class="statement" id="stage1"><span class="statement-title"><i class="statement-title">阶段1。</我></span>符合LME纵向协变量数据模型,并估计缺失或量错反是;基于拟合模型。</gydF4y2Baspan></p> <p><span class="statement" id="stage2"><span class="statement-title"><i class="statement-title">阶段2。</我></span>符合的生存模式<我>分别</我>,缺失或未被注意的真正的协变量值代替他们估计从第一阶段作为观测值,然后进行生存分析。</gydF4y2Baspan></p> <p>主要优势的两阶段方法,包括修改的两阶段方法如下所述,是简单的,他们可以使用现有的软件来实现。这些方法的局限性是,他们可能会导致偏见的推理有几个原因。首先,在纵向协变量模型参数的估计,截断了的事件不合并。即纵向协变量轨迹的受试者经历事件可能不同于那些不经历这个事件,所以相关的参数估计与纵向协变量模型在第一阶段,仅基于观察协变量数据,可能会有偏见。第二,<我>不确定性</我>估计的不纳入第一阶段第二阶段生存模型的估计。因此,标准误差参数生存模型的估计可能被低估。第三,所有信息纵向过程和生存过程中不能完全以每个模型拟合结合产生最有效的估计。</p><p>gydF4y2Ba偏差引起的纵向模型参数的估计忽略了从事件可能取决于信息截断<我>协会的力量</我>之间的纵向过程和生存过程。偏差导致忽略了估计阶段的不确定性<gydF4y2Baa href="#stage1">1</gydF4y2Baa>可能取决于<我>测量误差的大小</我>协变量。为了解决这些问题,提出了各种改性两阶段方法,导致更好的两阶段方法。</p><p>gydF4y2Ba自我和Pawitan [<gydF4y2Baa href="#B36">18</gydF4y2Baa>)视为一个两阶段最小二乘法的方法被用来适应个体纵向协变量的轨迹;被用来估计嫁祸于生存的“真正”的协变量值模型和推理是基于通常的部分的可能性。Tsiatis et al。<gydF4y2Baa href="#B22">19</gydF4y2Baa>)被认为是一个近似风险函数,然后利用近似构造部分的可能性。他们取代了真正的协变量<gydF4y2Basvg height="16.262501" id="M50" style="vertical-align:-3.7982pt;width:29.5625px;" version="1.1" viewbox="0 0 29.5625 16.262501" width="29.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.64,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>经验贝叶斯估计的条件期望<gydF4y2Basvg height="18.25" id="M51" style="vertical-align:-3.7982pt;width:145.1375px;" version="1.1" viewbox="0 0 145.1375 18.25" width="145.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.25)"> <g transform="translate(72,-57.4)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9271421" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.090641" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-52.62,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.54,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.5054" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.79,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.87,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.617687" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.00696" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.034847" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,36.68,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.9,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="18.25" id="M52" style="vertical-align:-3.7982pt;width:141.825px;" version="1.1" viewbox="0 0 141.825 18.25" width="141.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.25)"> <g transform="translate(72,-57.4)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.78,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.745598" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.79,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.57,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.25342" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.020424" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.060814" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.974251" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>协变量的历史了吗<gydF4y2Basvg height="9.125" id="M53" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。他们获得了经验贝叶斯估计从标准符合LME模型的协变量的数据<gydF4y2Basvg height="9.125" id="M54" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>对所有受试者仍面临风险<gydF4y2Basvg height="9.125" id="M55" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。相似的两阶段方法也提出了Bycott和泰勒(<gydF4y2Baa href="#B32">20.</gydF4y2Baa>]和Dafni Tsiatis [<gydF4y2Baa href="#B33">21</gydF4y2Baa>]。</p><p>gydF4y2Ba最近,其他两阶段方法已经开发出来的文学作品。续集,我们回顾最近的一些方法。普伦蒂斯(后<gydF4y2Baa href="#B18">22</gydF4y2Baa>),我们重写生存模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>),<gydF4y2Baspan class="equation" id="EEq3"> <svg height="19.35" id="M56" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,36.69,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,43.46,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.76,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7634392" y="-2.51"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.314771" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,70.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,75.63,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.529686" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.63,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,132.76,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.72,61.14)"> <tspan style="font-size: 12.50px; " x="26.08" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.099998" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.950001" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.870001" y="0.0099999998"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.421333" y="0.0099999998"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.672832" y="0.0099999998"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.91,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,212.07,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,232.55,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.21,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.05,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.76,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,272.58,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.45,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.119129" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.81,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,305.12,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.529686" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,330.9,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,334.12,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,347.42,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,354.11,61.13)"> <tspan style="font-size: 12.50px; " x="15.95" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.82" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.64" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="114.8035" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.055" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="124.18075" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="130.43225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>其中包括一个棘手的条件期望。后Dafni和Tsiatis<gydF4y2Baa href="#B33">21</gydF4y2Baa>和你们et al。<gydF4y2Baa href="#B31">8</gydF4y2Baa>),我们近似上述条件期望<gydF4y2Baspan class="equation" id="EEq4"> <svg height="49.775002" id="M57" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.775002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.775)"> <g transform="translate(72,-32.18)"> <text transform="matrix(1,0,0,-1,71.77,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.76" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.77" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.619999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.549999" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.101332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.352833" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,122.63,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.79,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.28,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.93,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.78,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.49,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,190.3,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.18,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.121632" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.54,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.85,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.517183" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,248.63,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,251.85,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,265.14,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.83,61.13)"> <tspan style="font-size: 12.50px; " x="15.96" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-130.64" y="26.85"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-125.85" y="24.34"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-114.09" y="26.85"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-108.24" y="24.34"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-166.98" y="24.34"> ≈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-152.86412" y="24.34"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-147.31277" y="24.34"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-141.06128" y="24.34"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,169.83,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.99,36.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.312436" y="0.0099999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.48,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.13,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.98,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.69,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.5,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.85,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.89,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.19,36.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.324939" y="0.0099999998"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.526188" y="0.0099999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.98,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,293.2,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,306.49,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,313.18,36.79)"> <tspan style="font-size: 12.50px; " x="28.68" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.95" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.801405" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="151.57001" y="-12.17"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="155.73351" y="-12.17"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="161.985" y="-12.17"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="165.11075" y="-12.17"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.36224" y="-12.17"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>一个两阶段方法可以进行如下。在第一步中,我们估计条件期望<gydF4y2Basvg height="18.25" id="M58" style="vertical-align:-3.7982pt;width:218.2px;" version="1.1" viewbox="0 0 218.2 18.25" width="218.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.25)"> <g transform="translate(72,-57.4)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9271421" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.090641" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-52.62,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.54,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.14,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.49,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.64,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,3.07,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,10.88,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.23,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,32.27,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,35.49,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,59.19,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.41,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,75.7,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.39,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.953828" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>通过拟合协变量模型(<gydF4y2Baa href="#EEq2">2.2</gydF4y2Baa>)观察到的纵向数据和生存数据。在第二步中,然后替代条件期望(<gydF4y2Baa href="#EEq4">3.2</gydF4y2Baa>)(<gydF4y2Baa href="#EEq3">3.1</gydF4y2Baa>从第一步)的估计,然后我们进行标准推理Cox模型。你们et al。<gydF4y2Baa href="#B31">8</gydF4y2Baa>)提出了两种方法的第一步,叫道<我>风险回归校正(RRC)</我>方法和<我>普通回归校正(兽人)</我>方法,分别。这个想法是为了符合LME协变量模型(<gydF4y2Baa href="#EEq2">2.2</gydF4y2Baa>)观察到的协变量数据风险组或所有观察到的协变量数据。</p><p>gydF4y2Ba注意偏差的天真的两阶段方法造成的协变量的轨迹跟踪的长度有关。例如,受试者退出早期或死亡早期可能有不同的轨迹比那些在这项研究。因此,大部分的偏见可能会被删除,如果我们可以夺回这些失踪的协变量测量由于截断通过合并事件时间信息。艾伯特和施<gydF4y2Baa href="#B1">9</gydF4y2Baa>]提出夺回丢失的测量通过生成数据的条件分布的协变量的事件时间:<gydF4y2Baspan class="equation" id="eq2"> <svg height="35.587502" id="M59" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.587502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.5875)"> <g transform="translate(72,-43.53)"> <text transform="matrix(1,0,0,-1,89.7,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.53" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.379999" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.63,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.32,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,130.62,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.84,54.64)"> <tspan style="font-size: 12.50px; " x="12.64" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.959999" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34" y="7.6999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.09" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.610001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.459999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.85,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.55,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,218.6,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.82,54.64)"> <tspan style="font-size: 12.50px; " x="12.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.57" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.09" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.939999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,265.01,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.71,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.01,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,287.23,54.64)"> <tspan style="font-size: 12.50px; " x="12.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.57" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.221596" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,320.7,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,323.92,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="140.83" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="144.9935" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="151.245" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="154.37074" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="160.62225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>的协变量<gydF4y2Basvg height="11.3625" id="M60" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.3625" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>时间和事件<gydF4y2Basvg height="11.05" id="M61" style="vertical-align:-3.2316pt;width:11.025px;" version="1.1" viewbox="0 0 11.025 11.05" width="11.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>认为是条件独立的随机效应<gydF4y2Basvg height="11.55" id="M62" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="11" id="M63" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>包含所有未知参数。他们近似条件密度<gydF4y2Basvg height="14.9375" id="M64" style="vertical-align:-3.2316pt;width:69.712502px;" version="1.1" viewbox="0 0 69.712502 14.9375" width="69.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.08,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>使用LME模型,然后使用标准软件来模拟缺失的数据<gydF4y2Basvg height="14.9375" id="M65" style="vertical-align:-3.2316pt;width:69.712502px;" version="1.1" viewbox="0 0 69.712502 14.9375" width="69.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-33.08,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。一旦失踪的模拟测量,协变量模型然后安装到“完整的数据,用于第二步。过程是迭代多次将丢失的数据的不确定性。因此,我们的想法是类似于多个nonignorable归责方法缺失的数据。这种方法可以减少偏见导致截断。</p><p>gydF4y2Ba将估计的不确定性在第一步中,我们可以考虑<我>参数引导方法</我>如下。</p><p><gydF4y2Baspan class="statement" id="step1"><span class="statement-title"><i class="statement-title">步骤1。</我></span>基于假设协变量模型生成协变量值,估计未知参数替换。</gydF4y2Baspan></p> <p><span class="statement" id="step2"><span class="statement-title"><i class="statement-title">步骤2。</我></span>从安装生成生存时代的生存模式。</gydF4y2Baspan></p> <p><span class="statement" id="step3"><span class="statement-title"><i class="statement-title">步骤3。</我></span>为每个生成的引导数据集的步骤<gydF4y2Baa href="#step1">1</gydF4y2Baa>和<gydF4y2Baa href="#step2">2</gydF4y2Baa>使用两阶段方法,符合模型和获得新的参数估计。</gydF4y2Baspan></p> <p>重复这个过程<gydF4y2Basvg height="10.325" id="M66" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>次(说,<gydF4y2Basvg height="11.1" id="M67" style="vertical-align:-0.17555pt;width:53.837502px;" version="1.1" viewbox="0 0 53.837502 11.1" width="53.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.165419" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.205809" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.708809" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>),我们可以获得的标准错误的固定参数样本的协方差矩阵<gydF4y2Basvg height="10.325" id="M68" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>引导数据集。这个引导方法可能产生更可靠的标准误差比天真的两阶段方法如果假定的模型是正确的。</p><p>gydF4y2Ba有轴承的两阶段方法<我>回归校正</我>方法测量误差文学。许多这样的两阶段方法可能不会完全消除偏见。此外,他们依靠一定的假设和近似。这些假设的有效性,这些近似的准确性需要进一步调查。</p><gydF4y2Bah4 id="likelihood-methods">4所示。可能的方法</gydF4y2Bah4> <p>可能性的方法可能是使用最广泛的文献方法的联合模型。它提供了一个统一的方法来推断,产生有效的和最有效的推理,如果假定模型是正确的。可能性的方法是基于纵向数据和生存的可能性。然而,由于可以复杂,似然函数的一个主要挑战的可能性方法计算。</p><gydF4y2Bah5 id="sec4.1">4.1。的可能性</gydF4y2Bah5> <p>所有的观测数据<gydF4y2Basvg height="14.775" id="M69" style="vertical-align:-3.2316pt;width:185.1875px;" version="1.1" viewbox="0 0 185.1875 14.775" width="185.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.164939" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.87,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-54.65,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.65,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.43,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-29.67,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.45,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.99,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.77,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.528246" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.932903" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.184402" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.398151" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.649654" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.850903" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.441902" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.655655" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.869644" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="14.8875" id="M70" style="vertical-align:-3.25793pt;width:125.55px;" version="1.1" viewbox="0 0 125.55 14.8875" width="125.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.743917" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.907415" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.72179" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.935543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.237534" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.451286" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.790543" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.991791" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.956444" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.170197" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.35,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.23,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>表示的集合中所有未知参数模型<gydF4y2Basvg height="14.8875" id="M71" style="vertical-align:-3.25793pt;width:180.52499px;" version="1.1" viewbox="0 0 180.52499 14.8875" width="180.52499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.82,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.48,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.67,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.8,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.72,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.5,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.528246" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.932903" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.184402" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.398151" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.649654" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.850903" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.441902" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.655655" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.869644" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>。我们假定生存数据的审查和评估过程的纵向noninformative测量。(总体)所有的观测数据的可能性<gydF4y2Baspan class="equation" id="EEq5"> <svg height="48.362499" id="M72" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3625)"> <g transform="translate(72,-33.31)"> <text transform="matrix(1,0,0,-1,45.82,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.091121" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.807152" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,95,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87.67,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.63,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,108.78,41.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0799999" y="-7.6999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-5.1799998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.459999" y="-7.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.15,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,141.37,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,152.37,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,159.06,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.66,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.74,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,189.07,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.95,49.67)"> <tspan style="font-size: 12.50px; " x="13.02" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.959999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.48" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.330002" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.83,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,243.53,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,256.58,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.8,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.50324" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,285.86,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,290.73,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.459999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.309999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,321.29,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,327.99,49.67)"> <tspan style="font-size: 12.50px; " x="15.76" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.700001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.351597" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,364.59,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,367.81,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.940002" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.1035" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.355" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.48075" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.73225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Baspan class="equation" id="eq3"> <svg height="193.2" id="M73" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 193.2" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,193.2)"> <g transform="translate(72,82.56)"> <text transform="matrix(1,0,0,-1,33.18,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.52" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.47,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,56.69,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.69,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,74.38,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,86.98,63.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,92.05,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.39,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.27,58.57)"> <tspan style="font-size: 12.50px; " x="13.02" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.34" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.380001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.169998" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,155.2,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.16,56.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.93,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.15,56.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.15" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.009998" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.481332" y="-2.51"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.732832" y="-2.51"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.4,63.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,224.55,56.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.32,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.54,56.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,251.64,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.29,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.14,63.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.85,58.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,290.01,55.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,294.89,56.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,305.53,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,309.58,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,140.88,26.05)"> <tspan style="font-size: 12.50px; " x="35.09" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.439999" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.09" y="7.6999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.865587" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.668419" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,199.97,40.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.71,37.89)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.72,14.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.73,26.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,214.5,22.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.46,26.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.509998" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.360001" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.03665" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.275646" y="0.0099999998"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.826979" y="0.0099999998"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.07848" y="0.0099999998"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.06,31.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.22,23.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.98,22.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,293.2,23.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.3,22.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,314.95,26.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,332.8,31.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,339.51,26.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,345.67,22.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.55,23.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.459999" y="4.8200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.9" y="-2.51"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-304.09" y="42.540001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-293.56" y="45.049999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-287.70999" y="42.540001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.581596" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.39,-22.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,75.08,-19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.8016319" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.13,-22.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,91.35,-19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.515743" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.42,-13.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,122.29,-21.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.360001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.209999" y="-2.51"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.461498" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.063324" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,170.7,-13.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.57,-21.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.42,-11.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.63,-13.55)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,196.07,-11.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.4330561" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.46,-19)"> <tspan style="font-size: 12.50px; " x="22.23" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.49" y="3.5527137e-015"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.25" y="-8.0699997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.099998" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.11,-11.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,263.11,-8.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.26,-3.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,285.33,-10.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,291.18,-0.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.98,-10.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,311.38,-11.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,317.38,-8.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,334.53,-3.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,339.6,-10.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 245.71,-15.87 99.74,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,286.35,-28.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.94,-24.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,346.65,-28.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.35" y="-9.7299995"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-269.44" y="37.68"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-258.92001" y="40.189999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-253.07001" y="37.68"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.83,-69.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,106.53,-66.41)"> <tspan style="font-size: 12.50px; " x="15.76" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.08" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.119999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.91" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.91" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.41" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.379997" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.379997" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.879997" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.970001" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.2215" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.26,-58.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.804176" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,205.02,-66.41)"> <tspan style="font-size: 12.50px; " x="22.219999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.49" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.25" y="-8.0699997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.099998" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.37,-50.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.08,-55.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.05,-50.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.92,-55.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,290.17,-58.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,293.39,-58.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 245.27,-63.28 53.97,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,269.13,-75.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.299999" y="0.98000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.650002" y="-8.75"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="195.62" y="-66.760002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="199.78349" y="-66.760002"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="206.035" y="-66.760002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="209.16075" y="-66.760002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="215.41225" y="-66.760002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>参数估计可以根据观测数据的可能性<gydF4y2Basvg height="13.6" id="M74" style="vertical-align:-2.21957pt;width:30.450001px;" version="1.1" viewbox="0 0 30.450001 13.6" width="30.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6)"> <g transform="translate(72,-61.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.8521242" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.092321" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>通过最大似然方法。注意,基线风险<gydF4y2Basvg height="14.75" id="M75" style="vertical-align:-3.25793pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 14.75" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>Cox模型是未指定的。它可以使用非参数极大似然估计方法通过假设<gydF4y2Basvg height="14.75" id="M76" style="vertical-align:-3.25793pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 14.75" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>需要离散质量在每个故障时间<gydF4y2Basvg height="13.0125" id="M77" style="vertical-align:-3.2316pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 13.0125" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因此,参数向量的维数<gydF4y2Basvg height="14.8875" id="M78" style="vertical-align:-3.25793pt;width:15.125px;" version="1.1" viewbox="0 0 15.125 14.8875" width="15.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.82,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>等于独特的失败次数。考克斯半参数模型转化为参数模型,但它引入了一个重大的挑战因为标准(ml)极大似然估计的渐近理论可能不适用由于无限维的性质<gydF4y2Basvg height="14.8875" id="M79" style="vertical-align:-3.25793pt;width:15.125px;" version="1.1" viewbox="0 0 15.125 14.8875" width="15.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.82,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。</p><p>gydF4y2Ba毫升的模型参数可以通过直接观测数据日志或使用可能性最大化一个EM算法。由于观测数据日志可能涉及一个棘手的积分,直接最大化往往是基于高斯数值积分技术,如埃尔米特正交或蒙特卡罗方法。然而,这些方法可能非常计算密集型的维度难以察觉的随机效应<gydF4y2Basvg height="11.55" id="M80" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>不低。EM算法的稳定性和通用性而闻名,所以它被广泛用于联合模型的似然推理(<gydF4y2Baa href="#B23">1</gydF4y2Baa>,<gydF4y2Baa href="#B29">3</gydF4y2Baa>,<gydF4y2Baa href="#B19">11</gydF4y2Baa>,<gydF4y2Baa href="#B21">23</gydF4y2Baa>]。E-step以来一个EM算法仍然是一个棘手的积分,蒙特卡罗方法或拉普拉斯算子近似常用于近似的条件期望E-step。M-step,牛顿迭代法是经常使用。</p><p>gydF4y2Ba谢长廷et al。<gydF4y2Baa href="#B8">24</gydF4y2Baa>)指出,标准误差的估计参数<gydF4y2Basvg height="14.0375" id="M81" style="vertical-align:-2.5707pt;width:52.875px;" version="1.1" viewbox="0 0 52.875 14.0375" width="52.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0375)"> <g transform="translate(72,-60.77)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.452988" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.666739" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.481113" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.694864" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.034126" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>根据费舍尔信息矩阵可能有问题,因为半参数联合模型的性质。他们建议引导方法获得标准错误。</p><gydF4y2Bah5 id="sec4.2">4.2。计算问题</gydF4y2Bah5> <p>联合模型的似然推理的主要挑战是计算复杂度,因为数值方法和蒙特卡罗方法可以非常随机效应的维数时计算量<gydF4y2Basvg height="11.55" id="M82" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>不是小的。此外,收敛的EM算法有时可以是一个问题。Tsiatis和Davidian<gydF4y2Baa href="#B23">1</gydF4y2Baa>]和Tsiatis Davidian [<gydF4y2Baa href="#B38">25</gydF4y2Baa>)提出了一个替代方法,所谓的条件评分方法,没有随机效应分布的假设<gydF4y2Basvg height="11.55" id="M83" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。他们的方法对待<gydF4y2Basvg height="11.55" id="M84" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为“讨厌参数”,条件合适的“充分统计量”<gydF4y2Basvg height="11.55" id="M85" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。空调在这足够的统计将消除依赖条件分布的随机效应<gydF4y2Basvg height="11.55" id="M86" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。这种方法会导致一系列的无偏估计方程,类似于通常的偏似然得分方程或广义估计方程(天啊)。一定规律的条件下,得到的估计一致性和渐近正态的,尽管他们可能不是最有效的。此外,他们的方法是相对简单的实现。歌等。<gydF4y2Baa href="#B20">26</gydF4y2Baa>)考虑另一种方法放松的常态假设<gydF4y2Basvg height="11.55" id="M87" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。他们假定随机效应分布在一个类光滑密度的家庭,包括标准正态密度作为一个特例。他们使用的可能性推理方法通过EM算法,但计算比条件更加密集的评分方法。歌和王<gydF4y2Baa href="#B37">27</gydF4y2Baa>)也提出了一个地方纠正分数估计量和当地条件分数估计量,需要分配的假设底层真正的协变量。</p><p>gydF4y2Ba近似但计算更高效的方法进行联合模型也出现在文学,如那些基于拉普拉斯近似(例如,<gydF4y2Baa href="#B19">11</gydF4y2Baa>,<gydF4y2Baa href="#B28">12</gydF4y2Baa>,<gydF4y2Baa href="#B13">28</gydF4y2Baa>])。当集成的维度在联合模型的可能性很高,拉普拉斯近似提供远比数值或蒙特卡罗方法计算的优势。请注意,拉普拉斯近似误差的顺序<gydF4y2Basvg height="18.5" id="M88" style="vertical-align:-3.7982pt;width:46.662498px;" version="1.1" viewbox="0 0 46.662498 18.5" width="46.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5)"> <g transform="translate(72,-57.2)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1521959" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.315695" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.76,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.89,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,不能任意精确的对于一个给定的数据集,在哪里<gydF4y2Basvg height="11.05" id="M89" style="vertical-align:-3.2316pt;width:15.25px;" version="1.1" viewbox="0 0 15.25 11.05" width="15.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在各个测量个体的数量吗<gydF4y2Basvg height="9.9250002" id="M90" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因此,拉普拉斯近似适用如果单个测量的数量很大。基于泰勒级数近似的近似方法类似于拉普拉斯近似;也就是说,他们的性能改善<gydF4y2Basvg height="11.05" id="M91" style="vertical-align:-3.2316pt;width:15.25px;" version="1.1" viewbox="0 0 15.25 11.05" width="15.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>增加。</p><p>gydF4y2BaRizopoulos et al。<gydF4y2Baa href="#B19">11</gydF4y2Baa>)建议使用完整的指数拉普拉斯近似的E-step EM算法。相比标准(一阶)拉普拉斯近似,完整的指数拉普拉斯近似方法近似误差<gydF4y2Basvg height="18.5" id="M92" style="vertical-align:-3.7982pt;width:46.662498px;" version="1.1" viewbox="0 0 46.662498 18.5" width="46.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5)"> <g transform="translate(72,-57.2)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1521959" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.315695" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.76,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.89,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,需要更少的在各个纵向测量产生可靠的结果。李等人。<gydF4y2Baa href="#B13">28</gydF4y2Baa>)建议二阶拉普拉斯近似。然而,这些拉普拉斯近似方法无法控制近似误差的大小,与高斯求积或蒙特卡罗积分技术。</p><gydF4y2Bah4 id="bayesian-methods">5。贝叶斯方法</gydF4y2Bah4> <p>贝叶斯联合模型也被研究了由不同的作者,包括Faucett和托马斯(<gydF4y2Baa href="#B5">29日</gydF4y2Baa>),徐和Zeger<gydF4y2Baa href="#B30">15</gydF4y2Baa>],小王和泰勒[<gydF4y2Baa href="#B24">5</gydF4y2Baa>)、法律等。<gydF4y2Baa href="#B12">30.</gydF4y2Baa>),易卜拉欣et al。<gydF4y2Baa href="#B10">16</gydF4y2Baa>),和黄等。<gydF4y2Baa href="#B9">13</gydF4y2Baa>]。联合模型可能包含许多未知参数,在推理可能导致潜在的问题。贝叶斯方法的主要优势是,他们可以从类似研究借附加信息或从专家和整合这些信息在当前的分析,在当前模型参数的先验分布形式。因此,推理的贝叶斯方法可以非常有用的联合模型。</p><p>gydF4y2Ba为贝叶斯联合模型,模型参数假定遵循一些先验分布,然后推断是基于后验分布的观测数据。让<gydF4y2Basvg height="11" id="M93" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>表示联合模型中未知参数的收集,和让<gydF4y2Basvg height="13.75" id="M94" style="vertical-align:-2.34499pt;width:28.049999px;" version="1.1" viewbox="0 0 28.049999 13.75" width="28.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.75)"> <g transform="translate(72,-61)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.179361" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>表示先验分布。让<gydF4y2Basvg height="14.8875" id="M95" style="vertical-align:-3.2316pt;width:218.41251px;" version="1.1" viewbox="0 0 218.41251 14.8875" width="218.41251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.528486" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.568874" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.570316" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.733814" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.3,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.08,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-17.08,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.86,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.1,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.12,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.59,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,14.81,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.528246" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.932903" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.184402" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.385651" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.63715" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.850903" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.441902" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.64315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.85714" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>表示所有的观测数据。联合<我>后验分布</我>对所有未知参数<gydF4y2Basvg height="11" id="M96" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和随机效应<gydF4y2Basvg height="14.775" id="M97" style="vertical-align:-3.2316pt;width:136.97501px;" version="1.1" viewbox="0 0 136.97501 14.775" width="136.97501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.75666" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-37.93,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.71,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.769403" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.020905" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.222153" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.813152" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.026901" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.240891" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>然后由<gydF4y2Baspan class="equation" id="eq4"> <svg height="48.362499" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3625)"> <g transform="translate(72,-33.31)"> <text transform="matrix(1,0,0,-1,21.59,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.968971" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.497936" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.563091" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.189922" y="0"> ∝</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,103.17,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,95.83,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.79,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.94,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.79" y="-2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.31" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.16" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.01,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,145.23,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.23,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.93,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.53,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.6,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.06,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,195.28,49.67)"> <tspan style="font-size: 12.50px; " x="12.29" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.23" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.75" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.599998" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.43,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.12,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.8016319" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.18,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.4,49.67)"> <tspan style="font-size: 12.50px; " x="12.28" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.219999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.74" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.59" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,303.24,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,309.94,49.67)"> <tspan style="font-size: 12.50px; " x="28.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.009998" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.76" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.611404" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.860001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.400028" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.20166" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,379.22,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,384.1,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.650002" y="-2.52"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.813499" y="-2.52"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.065002" y="-2.52"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.19075" y="-2.52"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.44225" y="-2.52"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="14.8875" id="M99" style="vertical-align:-3.25793pt;width:15.0625px;" version="1.1" viewbox="0 0 15.0625 14.8875" width="15.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.87,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>hyperparameters。贝叶斯推理是基于蒙特卡罗采样的后验分布<gydF4y2Basvg height="13.8625" id="M100" style="vertical-align:-2.37006pt;width:69.050003px;" version="1.1" viewbox="0 0 69.050003 13.8625" width="69.050003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.179361" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.38061" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.107944" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.909576" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.974731" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>吉布斯采样器等获得使用一个模型算法。例如,参数的后验均值和方差可以估计基于蒙特卡罗样品,和贝叶斯推理可以基于这些估计后验均值和方差。这蒙特卡罗抽样可以通过使用公开可用WinBUGS软件(<gydF4y2Baa href="#B15">31日</gydF4y2Baa>),这是相当一般,灵活、易于使用。</p><p>gydF4y2Ba像其他的贝叶斯方法,需要检查的最终结果是敏感的选择先验分布。有时候,在缺乏先验信息的情况下,noninformative先验或平面先验可能是可取的。</p><gydF4y2Bah4 id="other-joint-models">6。其他联合模型</gydF4y2Bah4> <p>在前面的章节中,我们专注于联合模型基于Cox模型right-censored生存数据和LME模型纵向数据。其他模型的生存数据和纵向数据也可以被认为是在关节模型。例如,对于生存数据,我们可以考虑加速失效时间间隔(AFT)模型和模型审查为复发事件数据和模型。纵向数据、非线性广义线性混合模型或半参数/非参数混合模型可以利用。尽管可以使用不同的生存模式和纵向模型,推理的基本思想和方法仍然是基本相同的。在下面,我们简短地回顾一下这些共同的模型。</p><gydF4y2Bah5 id="sec6.1">6.1。联合模型基于LME模型和一个尾模型</gydF4y2Bah5> <p>在纵向和生存数据的联合建模,我们可以使用尾模型特性的生存数据。在这里,我们专注于一个尾模型协变量与时间测量误差。纵向数据,我们再考虑LME模型简单。下面的描述是基于曾et al。<gydF4y2Baa href="#B21">23</gydF4y2Baa>]。船尾半参数模型可以用一种类似于Cox模型:<gydF4y2Baspan class="equation" id="EEq6"> <svg height="39.174999" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.174999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.175)"> <g transform="translate(72,-40.66)"> <text transform="matrix(1,0,0,-1,76.6,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.81,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,89.12,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.700269" y="0.0099999998"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.740658" y="0.0099999998"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,124.08,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.04,45.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3499999" y="0.37"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,144.39,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.1,52.96)"> <tspan style="font-size: 12.50px; " x="22.219999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.41" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.974556" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,194.32,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.48,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.309999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.16" y="7.3400002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.82" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.086422" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.325418" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.580002" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.231598" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.599998" y="0.0099999998"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.151333" y="0.0099999998"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.402832" y="0.0099999998"> p</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.010002" y="0.0099999998"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.574554" y="0.0099999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,299.29,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,306.45,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.299999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0834389" y="0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.322436" y="0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.58" y="0.0099999998"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="158.3" y="0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="162.4635" y="0.0099999998"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="168.715" y="0.0099999998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.84074" y="0.0099999998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.09225" y="0.0099999998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="14.825" id="M102" style="vertical-align:-3.2316pt;width:28.4625px;" version="1.1" viewbox="0 0 28.4625 14.825" width="28.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.52,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>风险的函数吗<gydF4y2Basvg height="9.9250002" id="M103" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>th个人时间<gydF4y2Basvg height="9.125" id="M104" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="14.8625" id="M105" style="vertical-align:-3.25793pt;width:30.5375px;" version="1.1" viewbox="0 0 30.5375 14.8625" width="30.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.86,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是基线风险函数,<gydF4y2Basvg height="16.262501" id="M106" style="vertical-align:-3.7982pt;width:29.5625px;" version="1.1" viewbox="0 0 29.5625 16.262501" width="29.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.64,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是无法正确协变量的值在时间吗<gydF4y2Basvg height="9.125" id="M107" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。对观察到的测量<gydF4y2Basvg height="14.7125" id="M108" style="vertical-align:-3.2316pt;width:27.25px;" version="1.1" viewbox="0 0 27.25 14.7125" width="27.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.49,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,我们再考虑LME模型(<gydF4y2Baa href="#EEq2">2.2</gydF4y2Baa>)。</p><p>gydF4y2Ba曾et al。<gydF4y2Baa href="#B21">23</gydF4y2Baa>使用一个EM算法)提出了一个可能性的方法。给出所有观测数据的可能性<gydF4y2Baspan class="equation" id="EEq7"> <svg height="48.362499" id="M109" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3625)"> <g transform="translate(72,-33.31)"> <text transform="matrix(1,0,0,-1,46.19,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.091121" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.167818" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.807152" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,95.38,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.04,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,91.01,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.15,41.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.0900002" y="-7.6999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-5.1799998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.459999" y="-7.6999998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.53,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,141.75,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,152.74,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,159.44,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,172.04,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,177.11,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,189.54,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,194.41,49.67)"> <tspan style="font-size: 12.50px; " x="12.19" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.120001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.65" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.5" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.46,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,243.15,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,256.2,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.42,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.50324" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,285.48,54.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,290.36,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.459999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.309999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,320.92,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,327.61,49.67)"> <tspan style="font-size: 12.50px; " x="15.77" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.700001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.351597" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,364.21,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,367.43,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.32" y="0.14"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.4835" y="0.14"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.735" y="0.14"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.86075" y="0.14"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.11225" y="0.14"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="17.799999" id="M110" style="vertical-align:-3.2316pt;width:93.525002px;" version="1.1" viewbox="0 0 93.525002 17.799999" width="93.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8)"> <g transform="translate(72,-57.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.55,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.33,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.50324" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-6.27,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.4,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.9375" id="M111" style="vertical-align:-3.2316pt;width:55.087502px;" version="1.1" viewbox="0 0 55.087502 14.9375" width="55.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-54.6,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.9,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.75378" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是相同的(<gydF4y2Baa href="#EEq5">4.1</gydF4y2Baa>),<gydF4y2Baspan class="equation" id="eq5"> <svg height="51.387501" id="M112" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51.3875)"> <g transform="translate(72,-30.89)"> <text transform="matrix(1,0,0,-1,-11.78,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.53" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.379999" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,8.51,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,11.73,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,22.73,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.43,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.03,52.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,47.1,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,59.52,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,64.4,47.04)"> <tspan style="font-size: 12.50px; " x="12.19" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.51" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.549999" y="9.7399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.810001" y="7.1054274e-015"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,113.43,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.38,44.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.34" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.190001" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,147.49,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.71,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.841782" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,174.8,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,178.02,44.52)"> <tspan style="font-size: 12.50px; " x="32.860001" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.709999" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.32" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.709032" y="-13.09"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,220.65,54.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.87,57.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> </text> <g> <path d="m 229.43,66.27 5.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,229.43,57.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,235.23,64.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.7299995"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.3,57.61)"> <tspan style="font-size: 12.50px; " x="12.19" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 194.34,50.16 64,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,219.58,38.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.88,35.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,259.54,37.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,267.8,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,271.85,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.88,47.04)"> <tspan style="font-size: 12.50px; " x="22.219999" y="9.7399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.669998" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.32" y="7.6999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> x</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> p</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,330.2,61.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.64504" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.5594559" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,341.5,58.88)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,343.95,61.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ;</gydF4y2Batspan> </text> <g> <path d="m 346.38,67.12 4.06,0" style="fill:none;stroke:#000000;stroke-width:0.57800001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,346.38,61.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.44,65.64)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="6.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,354.21,61.07)"> <tspan style="font-size: 8.75px; " x="-25.26" y="25.530001"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.0628638" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,366.78,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,373.99,43.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,380.95,47.04)"> <tspan style="font-size: 12.50px; " x="28.91" y="9.7399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.450001" y="7.1054274e-015"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.089921" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.328918" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.980515" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.800003" y="-1.28"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.963501" y="-1.28"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.214996" y="-1.28"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.340752" y="-1.28"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="103.59225" y="-1.28"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="17.5625" id="M113" style="vertical-align:-3.2316pt;width:13.725px;" version="1.1" viewbox="0 0 13.725 17.5625" width="13.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.5625)"> <g transform="translate(72,-57.95)"> <g> <path d="m -71.95,69.87 5.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.15,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.7399998"> </gydF4y2Batspan> </text> </g> </g> </svg>表示协变量和历史<gydF4y2Basvg height="13.425" id="M114" style="vertical-align:-2.29482pt;width:10.2px;" version="1.1" viewbox="0 0 10.2 13.425" width="10.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个已知的函数。</p><p>gydF4y2Ba联合处理尾部结构造型设置是更加困难比Cox模型<gydF4y2Basvg height="16.262501" id="M115" style="vertical-align:-3.7982pt;width:110.2375px;" version="1.1" viewbox="0 0 110.2375 16.262501" width="110.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.93,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.71,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.72,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.02,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.42,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.35,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-5.92,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.05,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>更加复杂和基线功能<gydF4y2Basvg height="17.6" id="M116" style="vertical-align:-3.25793pt;width:96.474998px;" version="1.1" viewbox="0 0 96.474998 17.6" width="96.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.6)"> <g transform="translate(72,-57.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,58.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.86,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.065875" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.229374" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-37.72,58.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.5,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> </text> <g> <path d="m -28.94,69.87 5.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-28.94,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.14,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.7399998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-18.06,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>包括未知的数量<gydF4y2Basvg height="14.8625" id="M117" style="vertical-align:-3.2316pt;width:73.262497px;" version="1.1" viewbox="0 0 73.262497 14.8625" width="73.262497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.965371" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.481113" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.694864" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.659515" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.860764" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.82,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-17.6,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的情况,而这不是Cox模型。不能使用一点质量函数和质量分配给所有未经审查的生存时间<gydF4y2Basvg height="13.0125" id="M118" style="vertical-align:-3.2316pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 13.0125" width="9.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>基线风险的功能<gydF4y2Basvg height="14.8625" id="M119" style="vertical-align:-3.25793pt;width:15.2375px;" version="1.1" viewbox="0 0 15.2375 14.8625" width="15.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。换句话说,在Cox模型,基线风险<gydF4y2Basvg height="14.8625" id="M120" style="vertical-align:-3.25793pt;width:15.2375px;" version="1.1" viewbox="0 0 15.2375 14.8625" width="15.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>可以用点质量的参数集合,但是这种方法是不可行的尾模型协变量,因为它依赖通过函数<gydF4y2Basvg height="17.5625" id="M121" style="vertical-align:-3.2316pt;width:66.362503px;" version="1.1" viewbox="0 0 66.362503 17.5625" width="66.362503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.5625)"> <g transform="translate(72,-57.95)"> <text transform="matrix(1,0,0,-1,-71.95,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.064435" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.227934" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.81,58.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-52.59,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</gydF4y2Batspan> </text> <g> <path d="m -47.03,69.87 5.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-47.03,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.23,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="9.7399998"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.15,61.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。为了绕过这个问题,曾et al。<gydF4y2Baa href="#B21">23</gydF4y2Baa>)认为基线风险函数<gydF4y2Basvg height="14.8625" id="M122" style="vertical-align:-3.25793pt;width:15.2375px;" version="1.1" viewbox="0 0 15.2375 14.8625" width="15.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个阶跃函数,常量值之间的连续两次失败。</p><p>gydF4y2Ba曾et al。<gydF4y2Baa href="#B21">23</gydF4y2Baa>)使用蒙特卡罗EM算法获取毫升。该框架是在前一节中类似。他们用蒙特卡罗方法来近似E-step条件期望。M-step涉及更复杂的计算由于复杂的基线风险<gydF4y2Basvg height="14.8625" id="M123" style="vertical-align:-3.25793pt;width:15.2375px;" version="1.1" viewbox="0 0 15.2375 14.8625" width="15.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。获得毫升的标准误差,通常的渐近公式基于费舍尔信息矩阵可能有问题,所以他们用引导的方法。</p><gydF4y2Bah5 id="sec6.2">6.2。联合模型与区间的生存数据</gydF4y2Bah5> <p>在前面的部分中,我们主要集中在对审查生存数据和假设的<我>确切的</我>生存时间或审查时间观察。然而在实践中,我们通常无法观察到的生存和审查,但我们只知道事件发生在一定的时间间隔。这种被称为生存数据<我>讨论区间</我>。为简单起见,我们假设所有的人在同一时间评估。再一次,让<gydF4y2Basvg height="14.5875" id="M124" style="vertical-align:-3.2316pt;width:14.3125px;" version="1.1" viewbox="0 0 14.3125 14.5875" width="14.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个事件的时间(存活时间)<gydF4y2Basvg height="9.9250002" id="M125" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>与观测值,<gydF4y2Basvg height="11.05" id="M126" style="vertical-align:-3.2316pt;width:11.025px;" version="1.1" viewbox="0 0 11.025 11.05" width="11.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="17.762501" id="M127" style="vertical-align:-3.2316pt;width:114.575px;" version="1.1" viewbox="0 0 114.575 17.762501" width="114.575" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7625)"> <g transform="translate(72,-57.79)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.71,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.4,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.81,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.7,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,8.73,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,12.9,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>等指标向量的事件<gydF4y2Basvg height="16.637501" id="M128" style="vertical-align:-4.77652pt;width:42.637501px;" version="1.1" viewbox="0 0 42.637501 16.637501" width="42.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>如果主题<gydF4y2Basvg height="9.9250002" id="M129" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>有一个事件发生的时间吗<gydF4y2Basvg height="14.9375" id="M130" style="vertical-align:-4.77652pt;width:22.862499px;" version="1.1" viewbox="0 0 22.862499 14.9375" width="22.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>时间<gydF4y2Basvg height="14.9375" id="M131" style="vertical-align:-4.77652pt;width:10.55px;" version="1.1" viewbox="0 0 10.55 14.9375" width="10.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="16.637501" id="M132" style="vertical-align:-4.77652pt;width:42.637501px;" version="1.1" viewbox="0 0 42.637501 16.637501" width="42.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>否则,<gydF4y2Basvg height="12.8875" id="M133" style="vertical-align:-1.76814pt;width:85.537498px;" version="1.1" viewbox="0 0 85.537498 12.8875" width="85.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.108906" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.31015" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.901154" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.114902" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>;<gydF4y2Basvg height="13.6125" id="M134" style="vertical-align:-2.34499pt;width:90.087502px;" version="1.1" viewbox="0 0 90.087502 13.6125" width="90.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.832638" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.084137" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.285385" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.876389" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.090137" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。我们假设<gydF4y2Basvg height="14.7125" id="M135" style="vertical-align:-3.2316pt;width:43.200001px;" version="1.1" viewbox="0 0 43.200001 14.7125" width="43.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>对所有<gydF4y2Basvg height="9.9250002" id="M136" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="16.637501" id="M137" style="vertical-align:-4.77652pt;width:141.91251px;" version="1.1" viewbox="0 0 141.91251 16.637501" width="141.91251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.454668" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.618168" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-27.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.92,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,10.24,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,16.93,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,32.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,37.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Baspan class="equation" id="EEq8"> <svg height="19.6" id="M138" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,42.56,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,49.53,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,60.16,61.13)"> <tspan style="font-size: 12.50px; " x="23.42" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.27" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,93.34,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.09,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.26,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,137.95,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.9,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,161.8,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.73,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,183.42,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,199.37,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.65,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.119999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.970001" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.347885" y="-2.51"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.375051" y="-2.51"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.727776" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.75,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,287.44,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,303.39,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,311.29,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,326.22,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,332.91,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,348.86,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,363.13,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.62" y="-2.51"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="105.7835" y="-2.51"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.035" y="-2.51"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.16075" y="-2.51"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.41225" y="-2.51"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>然后,我们有<gydF4y2Basvg height="16.637501" id="M139" style="vertical-align:-4.77652pt;width:250.1875px;" version="1.1" viewbox="0 0 250.1875 16.637501" width="250.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.218552" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.558773" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.66,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.07,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,31.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> ⋯</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.904776" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.068275" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.435661" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9098721" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.3143997" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="14.30952" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.95,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。事件的概率函数指标向量<gydF4y2Basvg height="11.55" id="M140" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.55" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>可以写成<gydF4y2Baspan class="equation" id="EEq9"> <svg height="50.287498" id="M141" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.287498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.2875)"> <g transform="translate(72,-31.77)"> <text transform="matrix(1,0,0,-1,107.66,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.52" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.58,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,132.8,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.57,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.16,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.79,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,173.19,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.3,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.87,55.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.3,45.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.09,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.54,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.13,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,206.76,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="3.4045279" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="9.3996477" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.16,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,230.76,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.33,55.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,230.13,45.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.08,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.877166" y="-2.52"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.28,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.43,47.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.28,57.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,300.22,55.01)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,305.97,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="158.78" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="162.9435" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="169.19499" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="172.32076" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.57225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>这是伯努利分布的概率函数。我们可以介绍观察容易出错的协变量的值<gydF4y2Basvg height="11.3625" id="M142" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.3625" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3625)"> <g transform="translate(72,-62.91)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,真正价值<gydF4y2Basvg height="16.262501" id="M143" style="vertical-align:-3.7982pt;width:13.725px;" version="1.1" viewbox="0 0 13.725 16.262501" width="13.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.15,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> </g> </g> </svg>,并承担<gydF4y2Baspan class="equation" id="eq6"> <svg height="19.825001" id="M144" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.825001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.825)"> <g transform="translate(72,-56.14)"> <text transform="matrix(1,0,0,-1,118.64,60.95)"> <tspan style="font-size: 12.50px; " x="20.15" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.130001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.34" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.980053" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.455887" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.707386" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.990002" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.004662" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.357384" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.98,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.13,58.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.51" y="-2.51"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.537886" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.49,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.2,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,266.01,65.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,273.86,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,290.55,57.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,294.98,60.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="169.77" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="173.9335" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.185" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.31075" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="189.56226" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="14.0375" id="M145" style="vertical-align:-2.5707pt;width:9.8874998px;" version="1.1" viewbox="0 0 9.8874998 14.0375" width="9.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0375)"> <g transform="translate(72,-60.77)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.725" id="M146" style="vertical-align:-3.20526pt;width:105.9125px;" version="1.1" viewbox="0 0 105.9125 17.725" width="105.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.25246" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.292849" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.456348" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.14,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.26,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.993498" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.9,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,1.81,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.97,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是未知参数。然后,我们可以写的概率函数<gydF4y2Basvg height="11.55" id="M147" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.55" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>作为<gydF4y2Basvg height="16.262501" id="M148" style="vertical-align:-3.7982pt;width:87.887497px;" version="1.1" viewbox="0 0 87.887497 16.262501" width="87.887497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-30.93,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.229374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.018503" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。或者,我们可以假设<gydF4y2Basvg height="11.55" id="M149" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.55" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>取决于<gydF4y2Basvg height="16.262501" id="M150" style="vertical-align:-3.7982pt;width:13.725px;" version="1.1" viewbox="0 0 13.725 16.262501" width="13.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.15,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.6899996"> </gydF4y2Batspan> </text> </g> </g> </svg>只有通过随机效应<gydF4y2Basvg height="11.55" id="M151" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和写作的概率函数<gydF4y2Basvg height="11.55" id="M152" style="vertical-align:-3.2316pt;width:11.0875px;" version="1.1" viewbox="0 0 11.0875 11.55" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.4,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>作为<gydF4y2Basvg height="14.9375" id="M153" style="vertical-align:-3.2316pt;width:86.125px;" version="1.1" viewbox="0 0 86.125 14.9375" width="86.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.55,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.33,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.015623" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.229374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.018503" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</p><p>gydF4y2Ba让<gydF4y2Basvg height="14.9375" id="M154" style="vertical-align:-3.2316pt;width:87.425003px;" version="1.1" viewbox="0 0 87.425003 14.9375" width="87.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.3,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.6,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.55,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.33,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.50324" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.056252" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>条件概率密度函数,随机效应<gydF4y2Basvg height="11.55" id="M155" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="14.9375" id="M156" style="vertical-align:-3.2316pt;width:55.087502px;" version="1.1" viewbox="0 0 55.087502 14.9375" width="55.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-54.6,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.9,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.75378" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的边际概率密度函数<gydF4y2Basvg height="11.55" id="M157" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>与协方差矩阵<gydF4y2Basvg height="10.55" id="M158" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="11" id="M159" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>表示所有参数的集合模型。然后,<我>可能性</我>对所有观察到的数据可以写成<gydF4y2Baspan class="equation" id="EEq10"> <svg height="48.362499" id="M160" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.3625)"> <g transform="translate(72,-33.31)"> <text transform="matrix(1,0,0,-1,48.21,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,57.06,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.65,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.240197" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.867027" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.9,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.56,43.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,97.53,35.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.67,42.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3499999" y="0.37"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.44" y="-7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.959999" y="-4.8099999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.809999" y="-7.3299999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.04,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,159.73,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,172.78,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176,49.67)"> <tspan style="font-size: 12.50px; " x="26.059999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.990002" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.52" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.369999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.50324" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.716991" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.92,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.61,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.8016319" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,251.66,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.88,49.67)"> <tspan style="font-size: 12.50px; " x="25.030001" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.959999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.490002" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.34" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.028126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.229374" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,310.47,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,317.16,49.67)"> <tspan style="font-size: 12.50px; " x="15.77" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.700001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.351597" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,353.76,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,356.98,42.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.4399996" y="-7.3299999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.77" y="-7.3299999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.9335" y="-7.3299999"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="118.185" y="-7.3299999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.31075" y="-7.3299999"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="127.56225" y="-7.3299999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>标定的参数<gydF4y2Basvg height="11" id="M161" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>可以最大化的获得的观测数据可能性<gydF4y2Basvg height="14.8625" id="M162" style="vertical-align:-3.2316pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 14.8625" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.1,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-58.59,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.240197" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。由于观测数据的可能性<gydF4y2Basvg height="14.8625" id="M163" style="vertical-align:-3.2316pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 14.8625" width="36.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.1,60.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-58.59,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.240197" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>很难评估因其参与的棘手甚至高维积分,可以进行蒙特卡罗EM算法或其他更有效的近似计算方法。</p><gydF4y2Bah5 id="sec6.3">6.3。GLMM和NLME模型纵向数据</gydF4y2Bah5> <p>我们专注于LME造型纵向数据模型。其他模型的纵向数据也可以考虑。例如,一个可能考虑非线性mixed-effects (NLME)模型建模中的纵向数据联合模式(<gydF4y2Baa href="#B28">12</gydF4y2Baa>,<gydF4y2Baa href="#B27">32</gydF4y2Baa>]。NLME模型往往是机械的模型在某种意义上,它们通常是基于生成数据的潜在机制。另一方面,LME模型通常经验模型;也就是说,他们通常用于近似描述观测数据不考虑可能的数据生成机制。因此,科学NLME模型可能更可取,如果这样的模型存在。同样的,对于非正态的纵向数据,广义线性混合模型(GLMMs)认为,特殊的非线性模型,但本质上是经验模型。</p><p>gydF4y2Ba纵向模型是非线性时,两阶段方法的一般思想和方法进行联合模型仍然可以应用可能性。并发症是计算变得更加苛刻,因为纵向非线性的模型。</p><gydF4y2Bah5 id="sec6.4">6.4。联合模型缺失的数据</gydF4y2Bah5> <p>纵向数据、缺失值是很常见的。nonignorable缺失数据时,missingness概率可能与缺失的值或随机效应,缺失数据的过程往往是需要注册在推理过程中为了获得有效的结果。对于可能性的方法,直接将丢失的数据在联合模型推理机制。然而,计算变得更具挑战性。吴et al。<gydF4y2Baa href="#B28">12</gydF4y2Baa>,<gydF4y2Baa href="#B27">32</gydF4y2Baa>]认为缺失数据问题联合模型,利用蒙特卡洛EM算法和拉普拉斯近似。</p><gydF4y2Bah4 id="example-and-simulation">7所示。例子和仿真</gydF4y2Bah4> <h5 id="sec7.1">7.1。一个说明的例子</gydF4y2Bah5> <p>作为一个例子,我们考虑一个艾滋病数据集包括46个艾滋病毒感染患者的抗艾滋病病毒治疗。病毒载量(即。,pl作为米a HIV RNA) and CD4 cell count were repeatedly measured during the treatment. The number of viral load measurements for each individual varies from 4 to 10. It is known that CD4 is measured with substantial errors. About 11% viral load measurements are below the detection limit after the initial period of viral decay. We call the viral load below the detection limit as “viral suppression.” We wish to check if the initial CD4 trajectories are predictive for the time to viral suppression.</p><p>让<gydF4y2Basvg height="11.05" id="M164" style="vertical-align:-3.2316pt;width:11.025px;" version="1.1" viewbox="0 0 11.025 11.05" width="11.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是病毒抑制的时间,从一开始治疗的时间第一预定时间当病毒载量低于检出限。病毒抑制时间患者病毒载量不低于检出限可能被视为正确的审查,以研究结束时间为审查时间。我们使用两个模型,Cox模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)或尾模型(<gydF4y2Baa href="#EEq6">6.1</gydF4y2Baa>),病毒抑制功能的时间,<gydF4y2Basvg height="16.262501" id="M165" style="vertical-align:-3.7982pt;width:29.5625px;" version="1.1" viewbox="0 0 29.5625 16.262501" width="29.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.64,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是无法真正的CD4细胞计数的时间吗<gydF4y2Basvg height="9.125" id="M166" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>对个人<gydF4y2Basvg height="9.9250002" id="M167" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。这里我们不考虑其他协变量。</p><p>gydF4y2Ba解决时间的测量误差协变量CD4细胞计数,我们使用LME模型模型CD4轨迹:<gydF4y2Baspan class="equation" id="EEq11"> <svg height="19.6" id="M168" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,105.63,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> D</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.366667" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.25,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.87,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,164.31,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.96,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,189.58,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.18,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.969999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.82" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.55,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,237.21,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.83,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.42,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.35,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,275.5,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,300.85,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,308,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="156.75" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="160.9135" y="0"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="167.16499" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="170.29076" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="176.54225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>参数,随机效应和随机误差,假定分布前面的小节中描述的相同。固定的参数<gydF4y2Basvg height="14.75" id="M169" style="vertical-align:-3.25793pt;width:45.612499px;" version="1.1" viewbox="0 0 45.612499 14.75" width="45.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.73,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是人口CD4过程的截距和斜率和<gydF4y2Basvg height="14.7125" id="M170" style="vertical-align:-3.2316pt;width:51.724998px;" version="1.1" viewbox="0 0 51.724998 14.7125" width="51.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-53.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.43,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>从人口平均个体差异。为了避免非常小(大)估计,这可能是不稳定的,我们规范CD4细胞计数和重新调节原来的时间<gydF4y2Basvg height="9.125" id="M171" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(天),这样新的时间尺度是在0和1之间。我们使用联合估计模型参数模型法和两阶段法/引导标准误差修正。数量<gydF4y2Basvg height="11.1" id="M172" style="vertical-align:-0.17555pt;width:53.837502px;" version="1.1" viewbox="0 0 53.837502 11.1" width="53.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.165419" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.205809" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.708809" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>引导的样本。联合模型方法,我们认为Cox模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)和尾模型(<gydF4y2Baa href="#EEq6">6.1</gydF4y2Baa>),<gydF4y2Basvg height="14.8625" id="M173" style="vertical-align:-3.25793pt;width:30.112499px;" version="1.1" viewbox="0 0 30.112499 14.8625" width="30.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.86,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>威布尔的基线风险函数。另一方面,只有Cox模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)采用两阶段方法的比较。这些分析可以实现使用功能<gydF4y2Basvg height="13.6625" id="M174" style="vertical-align:-2.29482pt;width:49.4375px;" version="1.1" viewbox="0 0 49.4375 13.6625" width="49.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6625)"> <g transform="translate(72,-61.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.188745" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.915119" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.791769" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.905737" y="0"> ℎ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.119967" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M175" style="vertical-align:-2.21957pt;width:33.549999px;" version="1.1" viewbox="0 0 33.549999 13.45" width="33.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.9759541" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.853084" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.580418" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M176" style="vertical-align:-2.34499pt;width:84.400002px;" version="1.1" viewbox="0 0 84.400002 13.6125" width="84.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.590041" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.478474" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.692465" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.171417" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.897793" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.549389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.113224" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.252678" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在R软件。</p><p>gydF4y2Ba表<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/tab1/" target="_blank">1</gydF4y2Baa>介绍了主要参数的估计结果感兴趣的和他们的标准错误。我们可以看到从表<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/tab1/" target="_blank">1</gydF4y2Baa>在考克斯或船尾生存模型、两级和协变量的联合模型方法产生类似的估计(CD4)纵向模式。然而,两阶段方法可能低估了参数估计的标准误差,因为它不包含生存信息的估计过程。请注意,Cox模型和尾模型中的参数有不同的解释,由于不同的模型公式,所以他们不具有直接可比性。</p><gydF4y2Badiv class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="8"> <hr></td> </tr> <tr class="thead"> <td align="left">模型</gydF4y2Batd> <td align="center">方法</gydF4y2Batd> <td align="center"></td> <td align="center"> <svg height="14.625" id="M177" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 13.925 14.625" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="14.475" id="M178" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.925 14.475" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="11.075" id="M179" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.4125 11.075" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="10.925" id="M180" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.4125 10.925" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="6.9875002" id="M181" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg></td> </tr> <tr> <td class="thead-hr" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="4">Cox模型</gydF4y2Batd> <td align="center" rowspan="4">两级</gydF4y2Batd> <td align="center">估计</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.315</gydF4y2Batd> <td align="center">−0.233</gydF4y2Batd> <td align="center">1.345</gydF4y2Batd> <td align="center">0.605</gydF4y2Batd> </tr> <tr> <td align="center">SE</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.208</gydF4y2Batd> <td align="center">0.113</gydF4y2Batd> <td align="center">0.154</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center"> <svg height="10.325" id="M182" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>价值</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.129</gydF4y2Batd> <td align="center">0.040</gydF4y2Batd> <td align="center">< 0.001</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center">疯牛病</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.237</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="3">Cox模型</gydF4y2Batd> <td align="center" rowspan="3">联合模型</gydF4y2Batd> <td align="center">估计</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.648</gydF4y2Batd> <td align="center">−0.201</gydF4y2Batd> <td align="center">1.342</gydF4y2Batd> <td align="center">0.603</gydF4y2Batd> </tr> <tr> <td align="center">SE</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.234</gydF4y2Batd> <td align="center">0.135</gydF4y2Batd> <td align="center">0.162</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center"> <svg height="10.325" id="M183" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>价值</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">0.006</gydF4y2Batd> <td align="center">0.137</gydF4y2Batd> <td align="center">< 0.001</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="3">尾模型</gydF4y2Batd> <td align="center" rowspan="3">联合模型</gydF4y2Batd> <td align="center">估计</gydF4y2Batd> <td align="center">0.168</gydF4y2Batd> <td align="center">−0.487</gydF4y2Batd> <td align="center">−0.237</gydF4y2Batd> <td align="center">1.341</gydF4y2Batd> <td align="center">0.604</gydF4y2Batd> </tr> <tr> <td align="center">SE</gydF4y2Batd> <td align="center">0.260</gydF4y2Batd> <td align="center">0.289</gydF4y2Batd> <td align="center">0.125</gydF4y2Batd> <td align="center">0.156</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center"> <svg height="10.325" id="M184" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>价值</gydF4y2Batd> <td align="center">0.517</gydF4y2Batd> <td align="center">0.091</gydF4y2Batd> <td align="center">0.059</gydF4y2Batd> <td align="center">< 0.001</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr class="table-tr"> <td colspan="8"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> <tr class="table-fn"> <td>SE:标准误差;疯牛病:引导标准误差。的<gydF4y2Basvg height="10.325" id="M185" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>值是瓦尔德测试的测试是否对应的参数是0。<gydF4y2Babr></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2012/640153/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 艾滋病数据在不同的分析模型。</gydF4y2Badiv> </div> </div> <p>的参数<gydF4y2Basvg height="14.475" id="M186" style="vertical-align:-3.13504pt;width:13.925px;" version="1.1" viewbox="0 0 13.925 14.475" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>生存模型的措施的效果真的时间协变量CD4值活动时期,所以它的估计和相关的<gydF4y2Basvg height="10.325" id="M187" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>值可以用来检查是否真正的CD4值预测的时代病毒抑制。自协变量CD4是测量错误,解决测量误差的主要焦点联合建模在这个应用程序中。因此,估计<gydF4y2Basvg height="14.475" id="M188" style="vertical-align:-3.13504pt;width:13.925px;" version="1.1" viewbox="0 0 13.925 14.475" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>是主要的兴趣。联合模型方法,在考克斯或尾模型,有证据表明,CD4是协变量与时间相关病毒抑制测量误差后解决。发现的证据意义下的协变量的效果是最强的Cox模型。另一方面,两阶段方法可能严重低估了协变量CD4效果(小的价值<gydF4y2Basvg height="17.975" id="M189" style="vertical-align:-3.13504pt;width:14.9375px;" version="1.1" viewbox="0 0 14.9375 17.975" width="14.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-65.59,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.72"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,57.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>)。此外,天真的两阶段方法低估了的标准误差<gydF4y2Basvg height="17.975" id="M190" style="vertical-align:-3.13504pt;width:14.9375px;" version="1.1" viewbox="0 0 14.9375 17.975" width="14.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-65.59,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.72"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,57.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>由于未能将从第一步估计的不确定性。标准错误的低估程度上纠正引导方法。</p><gydF4y2Bah5 id="sec7.2">7.2。一个模拟研究</gydF4y2Bah5> <p>在本节中,我们进行仿真对比研究联合模型法和两阶段法/引导标准误差修正。我们从时间产生500数据集协变量CD4过程(<gydF4y2Baa href="#EEq11">7所示。1</gydF4y2Baa>在前一节的例子和Cox模型(<gydF4y2Baa href="#EEq1">2.1</gydF4y2Baa>)在恒定的基线风险函数<gydF4y2Basvg height="14.75" id="M191" style="vertical-align:-3.25793pt;width:57.174999px;" version="1.1" viewbox="0 0 57.174999 14.75" width="57.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-60.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>强调时间协变量的影响。仿真中使用的测量时间点是一样的那些在前一节的例子。模型参数的真实值,给定的表<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/tab2/" target="_blank">2</gydF4y2Baa>类似的例子,variance-covariance矩阵<gydF4y2Basvg height="10.55" id="M192" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>随机效应<gydF4y2Basvg height="11.55" id="M193" style="vertical-align:-3.2316pt;width:11.9625px;" version="1.1" viewbox="0 0 11.9625 11.55" width="11.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.55)"> <g transform="translate(72,-62.76)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.7,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>将对角线。再一次,我们把<gydF4y2Basvg height="11.1" id="M194" style="vertical-align:-0.17555pt;width:53.837502px;" version="1.1" viewbox="0 0 53.837502 11.1" width="53.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.165419" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.205809" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.708809" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>引导样品两阶段引导标准误差的方法。</p><gydF4y2Badiv class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="2">方法</gydF4y2Batd> <td align="center">参数</gydF4y2Batd> <td align="center"> <svg height="14.475" id="M195" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.925 14.475" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="11.075" id="M196" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.4125 11.075" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="10.925" id="M197" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.4125 10.925" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="6.9875002" id="M198" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="14.4625" id="M199" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 22.887501 14.4625" width="22.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg></td> <td align="center"> <svg height="14.4625" id="M200" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 22.887501 14.4625" width="22.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg></td> </tr> <tr> <td align="center">真正价值</gydF4y2Batd> <td align="center">0.6</gydF4y2Batd> <td align="center">−0.2</gydF4y2Batd> <td align="center">1。3</gydF4y2Batd> <td align="center">0.6</gydF4y2Batd> <td align="center">0.5</gydF4y2Batd> <td align="center">0.3</gydF4y2Batd> </tr> <tr> <td align="center" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="7">两级</gydF4y2Batd> <td align="center">美国东部时间</gydF4y2Batd> <td align="center">0.183</gydF4y2Batd> <td align="center">−0.183</gydF4y2Batd> <td align="center">1.303</gydF4y2Batd> <td align="center">0.598</gydF4y2Batd> <td align="center">0.501</gydF4y2Batd> <td align="center">0.353</gydF4y2Batd> </tr> <tr> <td align="center">ESE</gydF4y2Batd> <td align="center">0.216</gydF4y2Batd> <td align="center">0.111</gydF4y2Batd> <td align="center">0.164</gydF4y2Batd> <td align="center">0.025</gydF4y2Batd> <td align="center">0.114</gydF4y2Batd> <td align="center">0.209</gydF4y2Batd> </tr> <tr> <td align="center">日月光半导体</gydF4y2Batd> <td align="center">0.201</gydF4y2Batd> <td align="center">0.111</gydF4y2Batd> <td align="center">0.164</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center">疯牛病</gydF4y2Batd> <td align="center">0.250</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center">偏见</gydF4y2Batd> <td align="center">−0.417</gydF4y2Batd> <td align="center">0.017</gydF4y2Batd> <td align="center">0.003</gydF4y2Batd> <td align="center">−0.002</gydF4y2Batd> <td align="center">−0.001</gydF4y2Batd> <td align="center">0.053</gydF4y2Batd> </tr> <tr> <td align="center">均方误差</gydF4y2Batd> <td align="center">0.221</gydF4y2Batd> <td align="center">0.013</gydF4y2Batd> <td align="center">0.027</gydF4y2Batd> <td align="center">0.0007</gydF4y2Batd> <td align="center">0.013</gydF4y2Batd> <td align="center">0.046</gydF4y2Batd> </tr> <tr> <td align="center">CR</gydF4y2Batd> <td align="center">42.8</gydF4y2Batd> <td align="center">95.6</gydF4y2Batd> <td align="center">94.4</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center" colspan="8"> <hr></td> </tr> <tr> <td align="left" rowspan="6">联合模型</gydF4y2Batd> <td align="center">美国东部时间</gydF4y2Batd> <td align="center">0.6004</gydF4y2Batd> <td align="center">−0.175</gydF4y2Batd> <td align="center">1.296</gydF4y2Batd> <td align="center">0.598</gydF4y2Batd> <td align="center">0.492</gydF4y2Batd> <td align="center">0.321</gydF4y2Batd> </tr> <tr> <td align="center">ESE</gydF4y2Batd> <td align="center">0.256</gydF4y2Batd> <td align="center">0.103</gydF4y2Batd> <td align="center">0.161</gydF4y2Batd> <td align="center">0.020</gydF4y2Batd> <td align="center">0.092</gydF4y2Batd> <td align="center">0.156</gydF4y2Batd> </tr> <tr> <td align="center">日月光半导体</gydF4y2Batd> <td align="center">0.249</gydF4y2Batd> <td align="center">0.099</gydF4y2Batd> <td align="center">0.163</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr> <td align="center">偏见</gydF4y2Batd> <td align="center">0.0004</gydF4y2Batd> <td align="center">0.025</gydF4y2Batd> <td align="center">−0.004</gydF4y2Batd> <td align="center">−0.002</gydF4y2Batd> <td align="center">−0.008</gydF4y2Batd> <td align="center">0.021</gydF4y2Batd> </tr> <tr> <td align="center">均方误差</gydF4y2Batd> <td align="center">0.066</gydF4y2Batd> <td align="center">0.011</gydF4y2Batd> <td align="center">0.026</gydF4y2Batd> <td align="center">0.0004</gydF4y2Batd> <td align="center">0.008</gydF4y2Batd> <td align="center">0.025</gydF4y2Batd> </tr> <tr> <td align="center">CR</gydF4y2Batd> <td align="center">95.6</gydF4y2Batd> <td align="center">95.8</gydF4y2Batd> <td align="center">95.2</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> <td align="center">- - - - - -</gydF4y2Batd> </tr> <tr class="table-tr"> <td colspan="8"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jps/2012/640153/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 对比的两阶段法和联合似然法通过仿真研究。</gydF4y2Badiv> </div> </div> <p>在表<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/tab2/" target="_blank">2</gydF4y2Baa>我们报告平均参数的仿真结果估计,(美国东部时间),实证标准错误(ESE),平均渐近标准错误(ASE)的平均引导标准错误(疯牛病),实证偏见(偏见),均方误差(MSE)和覆盖率(CR)的95%置信区间。我们可以看到从表<gydF4y2Baa href="//www.newsama.com/journals/jps/2012/640153/tab2/" target="_blank">2</gydF4y2Baa>两级和联合模型方法产生相似的参数估计(接近真实参数)除了协变量的影响<gydF4y2Basvg height="14.475" id="M201" style="vertical-align:-3.13504pt;width:13.925px;" version="1.1" viewbox="0 0 13.925 14.475" width="13.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。特别是,估计<gydF4y2Basvg height="17.975" id="M202" style="vertical-align:-3.13504pt;width:14.9375px;" version="1.1" viewbox="0 0 14.9375 17.975" width="14.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-65.59,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.72"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,57.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>基于联合模型方法非常接近其真实价值,而基于两阶段方法估计大约三分之一的它真正的价值,这表明两阶段方法可能低估了时间协变量影响严重。联合模型方法提供了更小的均方误差和更合理的覆盖率为95%的置信区间的两阶段方法。此外,两阶段方法可能低估的标准差<gydF4y2Basvg height="17.975" id="M203" style="vertical-align:-3.13504pt;width:14.9375px;" version="1.1" viewbox="0 0 14.9375 17.975" width="14.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-65.59,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.72"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.97,57.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>和引导校正标准误差似乎是可信的。</p><p>gydF4y2Ba从上面的结果,我们看到联合似然方法产生偏见的估计和更可靠的标准误差小于两阶段方法。这些结果具有重要意义。例如,如果一个使用Wald-type测试模型选择,可能方法将提供更多可靠的结果。然而,两阶段方法通常更简单和更快计算输出比似然方法估计。我们也可以比较这两种方法和贝叶斯方法。注意,然而,贝叶斯方法是等价的可能性方法当noninformative先知先觉。我们预计,贝叶斯方法有类似的可能性方法的性能。</p><gydF4y2Bah4 id="discussion">8。讨论</gydF4y2Bah4> <p>我们提供了一个简短回顾共同联合模型和推理方法。在实践中,当我们需要考虑一个纵向的过程和事件过程和怀疑,这两个进程可能是相关的,如生存协变量模型与时间或纵向模型用有用的辍学生,重要的是使用联合模型推理方法,以避免偏见的结果。模型选择的文献联合模型是相当有限的。在实践中,可以选择最好的纵向模型基于观察到的纵向数据,可以选择最好的生存模型基于生存数据,使用这些模型的标准模型选择过程。然后,我们指定合理的两个模型之间的联系,比如共享随机效应。选择推理方法,联合似然方法通常会产生最可靠的结果<我>如果</我>假定的模型和分布是正确的。另一方面,两阶段方法可以计算简单,许多现有的模型和方法对纵向数据可以很容易地适应和生存数据。然而,两阶段方法可能不会完全消除偏见的参数估计在某些情况下。</p><p>gydF4y2Ba当纵向协变量过程终止事件的时候,也就是说,当事件后的纵向值不可用,如死亡或辍学,反是;有时被称为<我>协变量内部时间</我>。有时,然而,纵向协变量信息和事件后可用。例如,CD4测量可能仍然可用后患者被诊断出患有艾滋病。这些有时被称为反是<我>外部协变量</我>。在联合模型中,重要的是要区分内部和外部的协变量时间。特别是,对于内部时间,联合模型更可取,因为单独分析在这种情况下可能会导致更严重的偏见。</p><p>gydF4y2Ba协变量生存模型与测量误差时间联合模型文献中得到太多的关注。另一个常见的情况是纵向模型用有用的辍学生,生存模型可用于模型的辍学的过程。这两种情况下都专注于描述纵向和生存之间的关系的过程。一些作者也认为联合模型的重点是更高效的推理生存模型,使用纵向数据作为辅助信息(<gydF4y2Baa href="#B30">15</gydF4y2Baa>,<gydF4y2Baa href="#B34">33</gydF4y2Baa>,<gydF4y2Baa href="#B35">34</gydF4y2Baa>]或假设纵向过程和生存过程都是由一个共同的潜在的过程(<gydF4y2Baa href="#B7">4</gydF4y2Baa>]。Nathoo和院长<gydF4y2Baa href="#B16">7</gydF4y2Baa>)被认为是一个有趣的联合模型中一个NLME模型用来模拟树木生长,与空间相关性。</p><p>gydF4y2Ba也可以扩展到联合模型<我>多变量情况下</我>,不止一个纵向流程和多个事件流程可同时进行设计。扩展通常概念简单,但是计算和实现可以比单变量情况下更乏味。看到亨德森et al。<gydF4y2Baa href="#B7">4</gydF4y2Baa>),徐和Zeger<gydF4y2Baa href="#B39">35</gydF4y2Baa>),和歌曲等。<gydF4y2Baa href="#B20">26</gydF4y2Baa>]。</p><p>gydF4y2Ba曾和蔡<gydF4y2Baa href="#B40">36</gydF4y2Baa>派生一些联合最大似然估计的渐近结果分析纵向数据和生存。他们表现出极大似然估计量的一致性,得到他们的渐近分布,表明在极大似然估计的联合分析semiparametrically高效。</p><p>gydF4y2Ba虽然在关节模型已经被广泛的研究在过去的二十年,联合模型的重要性已经越来越认可,联合模型还没有广泛应用于实践。主要原因可能是缺乏软件。最近,Dimitris Rizopoulos开发了一个名为R包<我>JM</gydF4y2Ba我>可以用来配合联合模型与普通纵向反应和事件时间下最大似然方法。各种选项的生存模型和优化/集成算法提供,如生存Cox模型和尾模型数据和Gauss-Hermite集成方法和拉普拉斯近似。</p><gydF4y2Bah4 id="acknowledgments">确认</gydF4y2Bah4> <p>作者感谢编辑和两个裁判帮助和建设性的意见。支持的研究部分加拿大自然科学和工程研究理事会(NSERC)发现赠款l .吴w·刘,g . y .易和NIAID / NIH AI080338和MSP /国家安全局格兰特h98230黄- 09 - 1 - 0053 y。</p></gydF4y2Badiv> <div class="xml-content"> <h4 class="references" id="references">引用</gydF4y2Bah4> <ol> <li id="B23">a . a . Tsiatis和m . Davidian“纵向联合建模的概述和比较数据,”<我>Statistica中央研究院</我>,14卷,第818 - 793页,2004年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=An%20overview%20of%20joint%20modeling%20of%20longitudinal%20and time-to-event%20data&author=A. A. Tsiatis &author=M. Davidian&publication_year=2004" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B2">诉De Gruttola和x m .涂”造型的CD4-lymphocyte计数和生存时间的关系,“<我>生物识别技术</我>,50卷,不。4、1003 - 1014年,1994页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.2307/2533439">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Modelling%20progression%20of%20CD4-lymphocyte%20count%20and%20its%20relationship%20to%20survival%20time&author=V. De Gruttola &author=X. M. Tu&publication_year=1994" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B29">m . s . Wulfsohn和A . A . Tsiatis”联合模型为生存和纵向数据测量错误,”<我>生物识别技术</我>,53卷,不。1,第339 - 330页,1997。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.2307/2533118">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=A%20joint%20model%20for%20survival%20and%20longitudinal%20data%20measured%20with%20error&author=M. S. Wulfsohn &author=A. A. Tsiatis&publication_year=1997" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0874.62140">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B7">r·亨德森和a·多布森,p·迪格”联合纵向测量造型和事件时间数据,”<我>生物统计学</我>1卷,第480 - 465页,2000年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Joint%20modelling%20of%20longitudinal%20measurements%20and%20event%20time%20data&author=R. Henderson&author=P. Diggle&author=&author=A. Dobson&publication_year=2000" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B24">王y和j·m·g·泰勒,“联合建模时间纵向和事件数据与应用程序,获得性免疫缺陷综合征”<我>美国统计协会杂志》上</我>,卷96,不。455年,第905 - 895页,2001年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1198/016214501753208591">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Jointly%20modeling%20longitudinal%20and%20event%20time%20data%20with%20application%20to%20acquired%20immunodeficiency%20syndrome&author=Y. Wang &author=J. M. G. Taylor&publication_year=2001" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1047.62115">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B3">j·丁和J.-L。王”,与非参数建模纵向数据乘法与生存数据,共同随机效应”<我>生物识别技术</我>,卷64,不。2、546 - 556年,2008页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2007.00896.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Modeling%20longitudinal%20data%20with%20nonparametric%20multiplicative%20random%20effects%20jointly%20with%20survival%20data&author=J. Ding &author=J.-L. Wang&publication_year=2008" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B16">f·s·Nathoo和c·b·迪恩”空间多态过渡模型纵向事件数据,”<我>生物识别技术</我>,卷64,不。1,p . 271 - 279、326、2008。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2007.00785.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Spatial%20multistate%20transitional%20models%20for%20longitudinal%20event%20data&author=F. S. Nathoo &author=C. B. Dean&publication_year=2008" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1132.62093">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B31">w .你们、林x和j·m·g·泰勒,“半参数模型的纵向测量和比较一致两阶段回归标定方法,”<我>生物识别技术</我>,卷64,不。4、1238 - 1246年,2008页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2007.00983.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Semiparametric%20modeling%20of%20longitudinal%20measurements%20and%20time-to-event%20data—a%20two-stage%20regression%20calibration%20approach&author=W. Ye&author=X. Lin&author=&author=J. M. G. Taylor&publication_year=2008" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1151.62093">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B1">艾伯特p s和j·h·施”,在估计纵向测量和比较数据之间的关系用一个简单的两阶段过程中,“<我>生物识别技术</我>,卷66,不。3、983 - 987年,2010页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2009.01324_1.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=On%20estimating%20the%20relationship%20between%20longitudinal%20measurements%20and%20time-to-event%20data%20using%20a%20simple%20two-stage%20procedure&author=P. S. Albert &author=J. H. Shih&publication_year=2010" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B11">h . Jacqmin-Gadda c . Proust-Lima j·m·g·泰勒,和d . Commenges”分数测试纵向结果和时间之间条件独立事件联合潜类模型中的类,“<我>生物识别技术</我>,卷66,不。1,11-19,2010页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2009.01234.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Score%20test%20for%20conditional%20independence%20between%20longitudinal%20outcome%20and%20time%20to%20event%20given%20the%20classes%20in%20the%20joint%20latent%20class%20model&author=H. Jacqmin-Gadda&author=C. Proust-Lima&author=J. M. G. Taylor&author=&author=D. Commenges&publication_year=2010" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B19">d . Rizopoulos韦贝克g . e . Lesaffre,“完全指数拉普拉斯近似联合建模的生存和纵向数据,”<我>皇家统计学会杂志》系列B</我>,卷71,不。3、637 - 654年,2009页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1467-9868.2008.00704.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Fully%20exponential%20Laplace%20approximations%20for%20the%20joint%20modelling%20of%20survival%20and%20longitudinal%20data&author=D. Rizopoulos&author=G. Verbeke&author=&author=E. Lesaffre&publication_year=2009" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B28">l .吴w·刘,x j .胡”联合推理HIV病毒动力学和免疫抑制测量误差的存在,”<我>生物识别技术</我>,卷66,不。2、327 - 335年,2010页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2009.01308.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Joint%20inference%20on%20HIV%20viral%20dynamics%20and%20immune%20suppression%20in%20presence%20of%20measurement%20errors&author=L. Wu&author=W. Liu&author=&author=X. J. Hu&publication_year=2010" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B9">y黄、g . Dagne和l .吴“贝叶斯推理联合艾滋病毒动力学模型比较和纵向数据和偏态和协变量测量错误,”<我>医学统计</我>,30卷,不。24日,第2946 - 2930页,2011年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1002/sim.4321">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Bayesian%20inference%20on%20joint%20models%20of%20HIV%20dynamics%20for%20time-to-event%20and%20longitudinal%20data%20with%20skewness%20and%20covariate%20measurement%20errors&author=Y. Huang&author=G. Dagne&author=&author=L. Wu&publication_year=2011" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B17">问:潘g . y .易,“边际治疗效果的评估方法相关的纵向和生存结果,“<我>统计和推理</我>。在出版社。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=An%20estimation%20method%20of%20marginal%20treatment%20effects%20on%20correlated longitudinal%20and%20survival%20outcomes&author=Q. Pan &author=G. Y. Yi" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B30">徐和s . l . Zeger“联合组成的纵向数据的分析措施和次重复的事件,“<我>英国皇家统计学会杂志》上的C系列</我>,50卷,不。3、375 - 387年,2001页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/1467-9876.00241">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Joint%20analysis%20of%20longitudinal%20data%20comprising%20repeated%20measures%20and%20times%20to%20events&author=J. Xu &author=S. L. Zeger&publication_year=2001" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1112.62312">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B10">j·g·易卜拉欣·m·陈,d . Sinha“贝叶斯方法联合建模的纵向和生存数据与应用程序癌症疫苗试验,”<我>Statistica中央研究院</我>,14卷,不。3、863 - 883年,2004页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Bayesian%20methods%20for%20joint%20modeling%20of%20longitudinal%20and%20survival%20data%20with%20applications%20to%20cancer%20vaccine%20trials&author=J. G. Ibrahim&author=M. Chen&author=&author=D. Sinha&publication_year=2004" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1073.62100">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B14">r . j . a, d·b·鲁宾<我>缺失的数据统计分析</我>在概率论与数理统计,威利系列,Wiley-Interscience,纽约,纽约,美国,第二版,2002年版。<gydF4y2Baspan class="reflinks"></span></li> <li id="B36">美国自我和y Pawitan”建模疾病进展的一个标志和疾病的发作,”<我>艾滋病流行病学:方法论的问题</我>:p .朱厄尔、k·迪茨和v . t .告别。,Birkhaauser,波士顿,质量,美国,1992年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Modeling%20a%20marker%20of%20disease%20progression%20and%20onset%20of%20disease&author=S. Self &author=Y. Pawitan&publication_year=1992" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B22">答:a . Tsiatis诉DeGruttola, m . s . Wulfsohn”建模生存纵向数据测量与误差的关系:应用程序生存和艾滋病患者的CD4计数,“<我>美国统计协会杂志》上</我>卷。90年,27-37,1995页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Modeling%20the%20relationship%20of survival%20to%20longitudinal%20data%20measured%20with%20error:%20applications%20to%20survival%20and%20CD4 counts%20in%20patients%20with%20AIDS&author=A. A. Tsiatis&author=V. DeGruttola&author=&author=M. S. Wulfsohn&publication_year=1995" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B32">p . Bycott和j·泰勒,“比较平滑技术CD4数据测量与误差时间Cox比例风险模型,”<我>医学统计</我>,17卷,不。18日,第2077 - 2061页,1998年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1002/(SICI)1097-0258(19980930)17:18<2061::AID-SIM896>3.0.CO;2-O">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=A%20comparison%20of%20smoothing%20techniques%20for%20CD4%20data%20measured%20with%20error%20in%20a%20time-dependent%20Cox%20proportional%20hazards%20model&author=P. Bycott &author=J. Taylor&publication_year=1998" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B33">g . Dafni和a . a . Tsiatis”评估临床结果指标测量误差时,“<我>生物识别技术</我>,54卷,不。4、1445 - 1462年,1998页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.2307/2533670">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Evaluating%20surrogate%20markers%20of%20clinical%20outcome%20when%20measured%20with%20error&author=U. G. Dafni &author=A. A. Tsiatis&publication_year=1998" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B18">r·l·普伦蒂斯”协变量测量错误和失败时间回归模型参数估计,“<我>生物统计学</我>,卷69,不。2、331 - 342年,1982页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1093/biomet/69.2.331">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Covariate%20measurement%20errors%20and%20parameter%20estimation%20in%20a%20failure%20time%20regression%20model&author=R. L. Prentice&publication_year=1982" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0523.62083">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B21">y . k .曾、f .谢长廷和j·l·王”联合建模的加速时间和纵向数据失败,”<我>生物统计学</我>,卷92,不。3、587 - 603年,2005页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1093/biomet/92.3.587">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Joint%20modelling%20of%20accelerated%20failure%20time%20and%20longitudinal%20data&author=Y. K. Tseng&author=F. Hsieh&author=&author=J. L. Wang&publication_year=2005" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1152.62380">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B8">f .谢长廷Y.-K。曾和J.-L。王”,联合建模的生存和纵向数据:可能性方法重新审视,“<我>生物识别技术</我>,卷62,不。4、1037 - 1043年,2006页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2006.00570.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Joint%20modeling%20of%20survival%20and%20longitudinal%20data:%20likelihood%20approach%20revisited&author=F. Hsieh&author=Y.-K. Tseng&author=&author=J.-L. Wang&publication_year=2006" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1116.62105">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B38">A . A . Tsiatis和m . Davidian“半参数估计量的协变量比例风险模型与纵向测量错误,”<我>生物统计学</我>,卷88,不。2、447 - 458年,2001页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=A%20semiparametric%20estimator%20for%20the%20proportional%20hazards%20model%20with%20longitudinal%20covariates%20measured%20with%20error&author=A. A. Tsiatis &author=M. Davidian&publication_year=2001" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B20">x的歌,m . Davidian和A . A . Tsiatis”可能性半参数的纵向联合建模方法和比较数据,”<我>生物识别技术</我>,卷。58岁的没有。4、742 - 753年,2002页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.0006-341X.2002.00742.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=A%20semiparametric%20likelihood%20approach%20to%20joint%20modeling%20of%20longitudinal%20and%20time-to-event%20data&author=X. Song&author=M. Davidian&author=&author=A. A. Tsiatis&publication_year=2002" target="_blank">谷歌学术搜索</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A1210.62132">Zentralblatt数学</gydF4y2Baa></span></li> <li id="B37">x的歌声,c . y .王”半参数方法的联合建模与时变系数,纵向和生存数据”<我>生物识别技术</我>,卷64,不。2、557 - 566年,2008页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1111/j.1541-0420.2007.00890.x">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Semiparametric%20approaches%20for%20joint%20modeling%20of%20longitudinal%20and%20survival%20data%20with%20time-varying%20coefficients&author=X. Song &author=C. Y. Wang&publication_year=2008" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B13">j . a . y . Lee Nelder, y Pawitan,<我>广义线性模型与随机效应:通过H-likelihood统一分析</我>卷,106<我>专著的统计数据和应用概率</我>查普曼&大厅/ CRC,伦敦,英国,2006年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1201/9781420011340">出版商的网站</gydF4y2Baa></span></li> <li id="B5">c . l . Faucett和特区托马斯”,同时造型审查生存数据和协变量重复测量:吉布斯抽样方法,”<我>医学统计</我>,15卷,不。15日,第1685 - 1663页,1996年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1002/(SICI)1097-0258(19960815)15:15<1663::AID-SIM294>3.0.CO;2-1">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Simultaneously%20modelling%20censored%20survival%20data%20and%20repeatedly%20measured%20covariates:%20a%20Gibbs%20sampling%20approach&author=C. L. Faucett &author=D. C. Thomas&publication_year=1996" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B12">n . j .法律,j·m·g·泰勒,和h . m .桑德勒,“纵向疾病进展的联合建模标记和故障时间过程的治疗,”<我>生物统计学</我>,3卷,第563 - 547页,2002年。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=The%20joint%20modeling%20of%20a%20longitudinal disease%20progression%20marker%20and%20the%20failure%20time%20process%20in%20the%20presence%20of%20cure&author=N. J. Law&author=J. M. G. Taylor&author=&author=H. M. Sandler&publication_year=2002" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B15">d . j . Lunn a托马斯:最好的,和斯皮格尔霍尔特d,“WinBUGS-a贝叶斯建模框架:概念、结构和可扩展性,”<我>统计和计算</我>,10卷,不。4、325 - 337年,2000页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=WinBUGS—a%20Bayesian%20modelling%20framework:%20concepts,%20structure,%20and%20extensibility&author=D. J. Lunn&author=A. Thomas&author=N. Best&author=&author=D. Spiegelhalter&publication_year=2000" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B27">l .吴x j·胡,h . Wu”非线性mixed-effects联合推理模型和事件在缺失数据的存在,”<我>生物统计学</我>,9卷,不。2、308 - 320年,2008页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1093/biostatistics/kxm029">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Joint%20inference%20for%20nonlinear%20mixed-effects%20models%20and%20time%20to%20event%20at%20the%20presence%20of%20missing%20data&author=L. Wu&author=X. J. Hu&author=&author=H. Wu&publication_year=2008" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B34">c . l . Faucett n .辛克物流和j·m·g·泰勒,“生存分析使用辅助变量通过多个归罪,艾滋病临床试验数据与应用程序,”<我>生物识别技术</我>,卷。58岁的没有。1,37-47,2002页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Survival%20analysis%20using%20auxiliary%20variables%20via%20multiple%20imputation,%20with%20application%20to%20AIDS%20clinical%20trial%20data&author=C. L. Faucett&author=N. Schenker&author=&author=J. M. G. Taylor&publication_year=2002" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B35">j·w·霍根和n . m . Laird,“基于模型的方法来分析不完整的纵向和故障时间数据,”<我>医学统计</我>,16卷,不。1 - 3、259 - 272年,1997页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=Model-based%20approaches%20to%20analysing%20incomplete%20longitudinal%20and%20failure%20time%20data&author=J. W. Hogan &author=N. M. Laird&publication_year=1997" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B39">徐和s . l . Zeger”多个替代终点的评价。”<我>生物识别技术</我>卷,57号1,第87 - 81页,2001。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://scholar.google.com/scholar_lookup?title=The%20evaluation%20of%20multiple%20surrogate%20endpoints&author=J. Xu &author=S. L. Zeger&publication_year=2001" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> <li id="B40">d .曾庆红和j . Cai”联合最大似然估计的渐近结果分析重复测量和生存时间,“<我>统计年鉴</我>,33卷,不。5,2132 - 2163年,2005页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1214/009053605000000480">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=Asymptotic%20results%20for%20maximum%20likelihood%20estimators%20in%20joint%20analysis%20of%20repeated%20measurements%20and%20survival%20time&author=D. Zeng &author=J. Cai&publication_year=2005" target="_blank">谷歌学术搜索</gydF4y2Baa></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</gydF4y2Bah4> <p>版权©2012吴朗等。这是一个开放分布式下文章<gydF4y2Baa rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</gydF4y2Baa>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</p></gydF4y2Badiv> </div> </article> </div> </div> </div> <div id="related-articles" class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 becpDt hrTitleRef">更多相关文章</gydF4y2Bah4>对本文没有相关内容可用。<gydF4y2Badiv id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 qBdVJ"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob 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height="24"><span class="text">下载引用</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dUABlg sc-BngTV hmDWcT ref_desktop" href="//www.newsama.com/journals/jps/2012/640153.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</gydF4y2Baspan><span class="sc-gkFcWv gWTCXQ">更多的</gydF4y2Baspan></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/jps/2012/640153.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"></a> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/jps/2012/640153.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> XML</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</gydF4y2Baspan><span class="sc-gkFcWv gWTCXQ">订单</gydF4y2Baspan></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<gydF4y2Baspan>16299年</gydF4y2Baspan> </div> <div> 下载<gydF4y2Baspan>6318年</gydF4y2Baspan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2012/640153" data-style="small_circle"></span>引用</gydF4y2Badiv> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</gydF4y2Bah3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2012/640153&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" 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