Joint modelling of longitudinal and survival outcomes has received increasing attention in the recent years, especially for most cancer and AIDS clinical trials. They have usually been modelled considering time to event response (survival outcome) or repeated measurements (longitudinal outcome) separately.
However, as both outcomes are observed in one subject, a joint modelling of longitudinal and survival outcomes can take into account the dependence between the two types of responses in contrast with the separate modelling. See e.g. Henderson, Diggle and Dobson (2000, Biostatistics 1, 465-480) and Guo and Carlin (2004, The American Statistician 58, 16-24). The former proposed a likelihood-based joint model using the EM algorithm based on a zero-mean latent bivariate Gaussian process, whereas the latter addressed the problem of joint analysis by proposing a Bayesian hierarchical model via Markov Chain Monte Carlo (MCMC) methods.
Our aim is to review and improve some these methods illustrating them with an AIDS study that relates the CD4 cells (longitudinal outcome) with time to death (survival outcome) in predicting the median survival time of HIV/AIDS patients. That and other quantities of interest may be estimate using MCMC methods implemented in the software WinBUGS. We show that the Bayesian joint model presents considerable improvements in the median survival time distributions when compared with those obtained through longitudinal and survival models separately.