Bayesian Models for Semicontinuous Outcomes in Rolling Admission Therapy Groups

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Abstract

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. Alcohol and other drug abuse are frequently treated in a group therapy setting. If 2 clients attend the some of the same sessions, we might expect that—on average—their posttreatment outcomes would be more similar than if they had not attended any sessions together. Hence, if participants are allowed to enroll in therapy on a rolling basis, irregular patterns of session attendance can induce complex relationships between participant outcomes. Statistical methods have been developed previously to account for rolling admission group therapy when the outcomes are normally distributed. In the case of alcohol and other drug use interventions, however, a substantial fraction of participants often report zero use after treatment. We extend previous work to build models that accommodate semicontinuous outcomes, which are a mixture of continuous and discrete distributions, for such situations. We find that modern Bayesian statistical methods and software allow users to efficiently estimate nonstandard models such as these. 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. We find that the intervention is associated with a drop in the probability of any drinking, but find no evidence of a change in the amount of drinking, conditional on some drinking.

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