Bayesian approach to analysing longitudinal bivariate binary data with informative dropout

To study the effect of methadone treatment in reducing multiple drug uses while controlling for their joint dependency and non-random dropout, we propose a bivariate binary model with a separate informative dropout (ID) model. In the model, the logit of the probabilities of each type of drug-use and dropout indicator as well as the log of the odds ratio of both drug-uses are linear in some covariates and outcomes. The model allows the evaluation of the joint probabilities of bivariate outcomes. To account for the heterogeneity of drug use across patients, the model is further extended to incorporate mixture and random effects. Parameter estimation is conducted using a Bayesian approach and is demonstrated using a methadone treatment data. A simulation experiment is conducted to evaluate the effect of including an ID modeling to parameters in the outcome models.