Keywords: Alcohol and other drug treatment, Vector autoregression, Group therapy
Alcohol and other drug abuse are frequently treated in a group therapy setting. If participants are allowed to enroll in therapy on a rolling basis, irregular patterns of participant overlap can induce complex correlations of participant outcomes. Previous work has accounted for common session attendance by modeling random effects for each therapy session, which map to participant outcomes via a multiple membership construction when modeling normally distributed outcome measures. We build on this earlier work by extending the models to semicontinuous outcomes, or outcomes that are a mixture of continuous and discrete distributions. This results in multivariate session effects, for which we allow temporal dependencies of various orders. We illustrate our methods using data from a group-based intervention to treat substance abuse and depression, focusing on the outcome of average number of drinks per day.