Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages

Many clinical trials and other medical and reliability studies generate both longitudinal (repeated measurement) and survival (time to event) data. Many well-established methods exist for analyzing such data separately, but these may be inappropriate when the longitudinal variable is correlated with patient health status, hence the survival endpoint (as well as the possibility of study dropout). To remedy this, an earlier article proposed a joint model for longitudinal and survival data, obtaining maximum likelihood estimates via the EM algorithm. The longitudinal and survival responses are assumed independent given a linking latent bivariate Gaussian process and available covariates. We develop a fully Bayesian version of this approach, implemented via Markov chain Monte Carlo (MCMC) methods. We use the approach to jointly model the longitudinal and survival data from an AIDS clinical trial comparing two treatments, didanosine (ddI) and zalcitabine (ddC). Despite the complexity of the model, we find it to be relatively straightforward to implement and understand using the WinBUGS software. We compare our results to those obtained from readily available alternatives in SAS Procs MIXED, NLMIXED, PHREG, and LIFEREG, as well as Bayesian analogues of these traditional separate likelihood methods. The joint Bayesian approach appears to offer significantly improved and enhanced estimation of median survival times and other parameters of interest, as well as simpler coding and comparable runtimes.