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

Abstract

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 (rolling) basis. Changes in therapy group membership induce a complex correlation structure among 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 modeling approach relaxes 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. A second feature specifies 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 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 behavioral therapy to reduce depressive symptoms among residential AOD treatment clients.

Keywords: Bayesian hierarchical models; Conditional autoregressive prior; Dirichlet process; Group therapy; Growth curve; Mental health; Substance abuse treatment.

Figure 1

Posterior means for session effects from MM(CAR) and MM(I) models

Figure 2

Comparison of Posterior Means of Client Growth Curves under LGM(1RE), LGM(2RE) and MM(CAR) for Randomly-selected Clients.

Figure 3

Predictive margins for the treatment effect of CBT versus usual care at 3 (left panel) and 6 (right panel) months. Segments reflect the 95% credible intervals and boxes represent the interquartile range of the marginal posterior distribution.