A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this paper. A regular joint model normally supposes there exist subject-specific latent random effects or classes shared by the longitudinal and time-to-event processes and the two processes are conditionally independent given these latent variables. Under this assumption, the joint likelihood of the two processes is straightforward to derive and their association, as well as heterogeneity among the population, are naturally introduced by the unobservable latent variables. However, because of the unobservable nature of these latent variables, the conditional independence assumption is difficult to verify. Therefore, besides the random effects, a time-varying bivariate copula is introduced to account for the extra time-dependent association between the two processes. The proposed model includes a regular joint model as a special case under some copulas. Simulation studies indicates the parameter estimators in the proposed model are robust against copula misspecification and it has superior performance in predicting survival probabilities compared to the regular joint model. A real data application on the Primary biliary cirrhosis (PBC) data is performed.

翻译：本文提出了一种时变二元Copula联合模型，该模型通过随机效应与时变二元Copula共同对每个时间点重复测量的纵向结果与生存数据进行联合建模。常规联合模型通常假设存在个体特异性潜在随机效应或由纵向过程与生存过程共享的潜在类别，且给定这些潜在变量后两个过程条件独立。在此假设下，两个过程的联合似然易于推导，其间的关联性以及总体中的异质性自然由不可观测的潜在变量引入。然而，由于这些潜在变量的不可观测性，条件独立性假设难以验证。因此，除随机效应外，本文引入时变二元Copula以刻画两个过程之间额外的时变关联。所提模型在某些Copula函数下可将常规联合模型包含为特例。模拟研究表明，所提模型中的参数估计对Copula误设具有稳健性，且在预测生存概率方面优于常规联合模型。本文对原发性胆汁性胆管炎（PBC）数据进行了实际应用分析。