Emura Takeshi, Nakatochi Masahiro, Murotani Kenta, Rondeau Virginie
1 Graduate Institute of Statistics, National Central University, Jhongli City, Taoyuan, Taiwan.
2 Center for Advanced Medicine and Clinical Research, Nagoya University Hospital, Japan.
Stat Methods Med Res. 2017 Dec;26(6):2649-2666. doi: 10.1177/0962280215604510. Epub 2015 Sep 18.
Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package.
在生物医学研究中，当肿瘤进展时间（如癌症复发）因信息性终末事件（如死亡）而被截尾时，常出现相依截尾情况。对于合并现有研究的荟萃分析，在半竞争风险下考虑了肿瘤进展与死亡之间的联合生存模型，该模型通过特定研究的脆弱性诱导依赖性。本文利用copulas函数，通过引入肿瘤进展与死亡之间个体内关联产生的额外依赖源，对联合脆弱模型进行了推广。新模型的实用价值在荟萃分析中尤为明显，在这些分析中，各研究中一致测量的协变量较少，因此存在残余依赖性。协变量效应通过Cox比例风险模型来设定，基线风险基于样条进行非参数建模。然后通过最大化惩罚对数似然函数获得估计量。我们还表明，当前方法可轻松修改以适用于竞争风险或复发事件数据，并可推广以适应左截断。进行了模拟以检验所提出估计量的性能。该方法应用于一项荟萃分析，以评估最近提出的一种用于卵巢癌患者生存的生物标志物CXCL12。我们在R语言的joint.Cox包中实现了我们提出的方法。
