Bayesian Non-Parametric Hierarchical Modeling for Multiple Membership Data in Grouped Attendance Interventions

Bayesian models for semicontinuous outcomes in rolling admission therapy groups

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. (PsycINFO Database Record

Bayesian restricted spatial regression for examining session features and patient outcomes in open-enrollment group therapy studies

Group-based interventions have been developed for treating patients across a range of health conditions. Enrollment into such groups often occurs on an open (or rolling) basis. Conditional autoregression modeling of random session effects has been proposed to account for the expected correlation in session effects associated with the overlap in patient participation session to session. However, when the analytic objective is to examine the relationship between a fixed-effect session feature and a patient outcome using conditional autoregression, confounding might arise if the fixed session feature of interest and the random session effects vary across sessions in similar ways, resulting in bias and inflated standard errors of a fixed-effect session feature of interest. Motivated by the goal of examining the relationships between outcomes and the session features of leader and session module theme, we applied restricted spatial regression to the analysis of patient outcomes collected from 132 participants in an open-enrollment group for treating depression among patients of a residential alcohol and other drug treatment program, adapting the approach to the multilevel data structure of open-enrollment group data. As compared with standard conditional autoregression, the restricted regression approach resulted in more precise estimates of regression coefficients of the module theme and leader predictor variables. The restricted regression approach provides an important analytic tool for group therapy researchers who are investigating the relationship between key components of open-enrollment group therapy interventions and patient outcomes.

Bayesian Semi- and Non-parametric Models for Longitudinal Data with Multiple Membership Effects in R

We introduce growcurves for R that performs analysis of repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each subject through the subject's participation in a set of multiple elements that characterize the intervention. In our motivating study design under which subjects receive a group cognitive behavioral therapy (CBT) treatment, an element is a group CBT session and each subject attends multiple sessions that, together, comprise the treatment. The sets of elements, or group CBT sessions, attended by subjects will partly overlap with some of those from other subjects to induce a dependence in their responses. The growcurves package offers two alternative sets of hierarchical models: 1. Separate terms are specified for multivariate subject and MM element random effects, where the subject effects are modeled under a Dirichlet process prior to produce a semi-parametric construction; 2. A single term is employed to model joint subject-by-MM effects. A fully non-parametric dependent Dirichlet process formulation allows exploration of differences in subject responses across different MM elements. This model allows for borrowing information among subjects who express similar longitudinal trajectories for flexible estimation. growcurves deploys "estimation" functions to perform posterior sampling under a suite of prior options. An accompanying set of "plot" functions allow the user to readily extract by-subject growth curves. The design approach intends to anticipate inferential goals with tools that fully extract information from repeated measures data. Computational efficiency is achieved by performing the sampling for estimation functions using compiled C++.