A time-varying bivariate copula joint model for longitudinal and time-to-event data

Abstract Due to the potential association between the longitudinal and time-to-event data, these two types of data are often jointly analysed to obtain less biased and more efficient inferences. A regular joint model (RJM) normally assumes 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 the 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, in addition to the time-invariant random effects, a time-varying bivariate copula is introduced to account for the extra time-dependent association between the two processes. The proposed time-varying bivariate copula joint model includes a RJM as a special case under specific copulas. Our study indicates the proposed model is robust to copula misspecification in parameter estimation and superior in predicting survival probabilities compared to a RJM. A real data application on the primary biliary cirrhosis data is used to illustrate the merits of this method.