Time-to-event semi-competing risk endpoints may be correlated when both events are occurring on the same individual. These events and the association between them may also be influenced by individual characteristics. In this paper, we propose copula survival models to estimate hazard ratios of covariates on the non-terminal and terminal events, along with the effects of covariates on the association between the two events. We use the Normal, Clayton, Frank and Gumbel copulas to provide a variety of association structures between the non-terminal and terminal events. We apply the proposed methods to model semi-competing risks of graft failure and death for kidney transplant patients. We find that copula survival models perform better than the Cox proportional hazards model when estimating the non-terminal event hazard ratio of covariates. We also find that the inclusion of covariates in the association parameter of the copula models improves the estimation of the hazard ratios.

翻译：生存时间终点中的半竞争风险事件可能在同一个体上发生且相互关联。这些事件及其关联性还可能受到个体特征的影响。本文提出Copula生存模型，用于估计协变量对非终端事件和终端事件的风险比，以及协变量对两事件关联性的影响。我们采用正态Copula、Clayton Copula、Frank Copula和Gumbel Copula构建非终端事件与终端事件之间的多种关联结构。将该方法应用于肾移植患者的移植物衰竭与死亡半竞争风险建模，研究发现：在估计协变量对非终端事件的风险比时，Copula生存模型优于Cox比例风险模型；同时，在Copula模型的关联参数中纳入协变量可改善风险比的估计效果。