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Bayesian Hierarchical Semiparametric Modeling of Longitudinal Post-treatment Outcomes from Open-enrollment Therapy Groups

There are several challenges to testing the effectiveness of group therapy-based interventions in alcohol and other drug use (AOD) treatment settings. Enrollment into AOD therapy groups typically occurs on an open (or rolling) basis. As the therapy group's membership changes over the course of any single client's tenure, this induces a complex correlation structure among client outcomes. The difficulties involved with modeling this correlation are exacerbated by having relatively small numbers of clients attending each therapy group session. Another challenge is that primary outcomes are measured after group therapy ends, so that each post-treatment datum reflects the effect of all sessions attended by a client. Since such data are relatively sparse for estimating the effect of any one session of an open-enrollment therapy group on client outcomes, it is important to model post-treatment outcomes data as parsimoniously as possible. However, the number of post-treatment outcomes assessments is typically very limited, which imposes constraints on how realistically longitudinal changes in client outcomes can be modeled. Our modeling strategy combines two novel applications of Bayesian hierarchical modeling to improve inference and model fit given the constraints imposed by data from AOD group therapy studies. First, we relax the assumption of independent random effects in the standard multiple membership model by employing conditional autoregression (CAR) to model correlation in random therapy group session effects associated with clients' attendance of common group therapy sessions. Second, we specify a longitudinal growth model under which the posterior distribution of client-specific random effects, or growth parameters, is modeled non-parametrically. The Dirichlet process prior helps us overcome parameter identification limitations of standard parametric growth models given limited numbers of longitudinal assessments. We motivate and illustrate our approach with a data set from a study of group cognitive behavioral therapy to reduce depressive symptoms among residential AOD treatment clients.