Joint analysis of longitudinal data comprising repeated measures and times to events

In biomedical and public health research, both repeated measures of biomarkers Y as well as times T to key clinical events are often collected for a subject. The scientific question is how the distribution of the responses [T, YIX] changes with covariates X [T/X] may be the focus of the estimation where Y can be used as a surrogate for T. Alternatively, T may be the time to drop-out in a study in which [YIX] is the target for estimation. Also, the focus of a study might be on the effects of covariates X on both T and Y or on some underlying latent variable which is thought to be manifested in the observable outcomes. In this paper, we present a general model for the joint analysis of [T, YIX] and apply the model to estimate [TIX] and other related functionals by using the relevant information in both T and Y. We adopt a latent variable formulation like that of Fawcett and Thomas and use it to estimate several quantities of clinical relevance to determine the efficacy of a treatment in a clinical trial setting. We use a Markov chain Monte Carlo algorithm to estimate the model's parameters. We illustrate the methodology with an analysis of data from a clinical trial comparing risperidone with a placebo for the treatment of schizophrenia.