Joint modeling of bivariate longitudinal and survival data in spouse pairs

We investigated the association between longitudinally measured depression scores and survival times simultaneously for paired spouse data from the Cardiovascular Health Study (CHS). We propose a joint model incorporating within pair correlations, both in the longitudinal and survival processes. We use bivariate linear mixed-effects models for the longitudinal processes, where the random effects are used to model the temporal correlation within each subject and the correlation across outcomes between subjects. For the survival processes, we incorporate gamma frailties into Weibull proportional hazards models to account for the correlation between survival times within pairs. The two sub-models are then linked through shared random effects, where the longitudinal and survival processes are conditionally independent given the random effects. Parameter estimates are obtained via the EM algorithm by maximizing the joint likelihood for the bivariate longitudinal and bivariate survival data. We use our method to model data where the use of bivariate longitudinal and survival sub–models are apropos but where there are no competing risks, that is, the censoring of one spouse’s time–to–mortality is not necessarily guaranteed by the death of the other spouse.