Bayesian joint modelling of longitudinal data on abstinence, frequency and intensity of drinking in alcoholism trials

In alcoholism research, several complementary outcomes are of interest:abstinence from drinking during a specific time frame, and, when the individual is drinking, frequency of drinking (the proportion of days on which drinking occurs) and intensity of drinking (the average number of drinks per drinking day). The outcomes are often measured repeatedly over time on the same subject and, although they are closely related, they are rarely modelled together. We propose a joint model that allows us to fit these longitudinal outcomes simultaneously, using correlated random effects to model the association between the outcomes and between repeated measurements on the same subject. The model has three parts: a logistic part for sustained abstinence over the period of interest, a truncated binomial part for frequency of drinking and a log-normal model for drinking intensity when drinking occurs. Because of the computational impracticality of fitting models with many random effects by using standard frequentist approaches, we use a Bayesian approach to fit the joint model. We also conduct a simulation study to investigate the gains in parameter estimate bias and mean-squared error associated with joint versus separate modelling. We illustrate the approach on data from an alcoholism clinical trial.