Bayesian Hierarchical Semiparametric Modelling of Longitudinal Post-Treatment Outcomes from Open Enrolment Therapy Groups

There are several challenges to testing the effectiveness of group-therapy-based interventions in alcohol and other drug use treatment settings. Enrolment into alcohol and other drug use therapy groups typically occurs on an open (rolling) basis. Changes in therapy group membership induce a complex correlation structure between client outcomes, with relatively small numbers of clients attending each therapy group session. Primary outcomes are measured post treatment, so each datum reflects the effect of all sessions attended by a client. The number of post-treatment outcomes assessments is typically very limited. The first feature of our modelling approach relaxes the assumption of independent random effects in the standard multiple-membership model by employing conditional auto-regression to model correlation in random-therapy-group session effects associated with clients' attendance of common group therapy sessions. A second feature specifies a longitudinal growth model under which the posterior distribution of client-specific random effects, or growth parameters, is modelled non-parametrically. The Dirichlet process prior helps to overcome 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 behavioural therapy to reduce depressive symptoms among residential alcohol and other drug use treatment clients.