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June 2013 Bayesian nonparametric hierarchical modeling for multiple membership data in grouped attendance interventions
Terrance D. Savitsky, Susan M. Paddock
Ann. Appl. Stat. 7(2): 1074-1094 (June 2013). DOI: 10.1214/12-AOAS620

Abstract

We develop a dependent Dirichlet process (DDP) model for repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each client through a sequence of elements which overlap with those of other clients on different occasions. Our interest concentrates on study designs for which the overlaps of sequences occur for clients who receive an intervention in a shared or grouped fashion whose memberships may change over multiple treatment events. Our motivating application focuses on evaluation of the effectiveness of a group therapy intervention with treatment delivered through a sequence of cognitive behavioral therapy session blocks, called modules. An open-enrollment protocol permits entry of clients at the beginning of any new module in a manner that may produce unique MM sequences across clients. We begin with a model that composes an addition of client and multiple membership module random effect terms, which are assumed independent. Our MM DDP model relaxes the assumption of conditionally independent client and module random effects by specifying a collection of random distributions for the client effect parameters that are indexed by the unique set of module attendances. We demonstrate how this construction facilitates examining heterogeneity in the relative effectiveness of group therapy modules over repeated measurement occasions.

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Terrance D. Savitsky. Susan M. Paddock. "Bayesian nonparametric hierarchical modeling for multiple membership data in grouped attendance interventions." Ann. Appl. Stat. 7 (2) 1074 - 1094, June 2013. https://doi.org/10.1214/12-AOAS620

Information

Published: June 2013
First available in Project Euclid: 27 June 2013

zbMATH: 1288.62166
MathSciNet: MR3113501
Digital Object Identifier: 10.1214/12-AOAS620

Keywords: Bayesian hierarchical models , Conditional autoregressive prior , Dirichlet process , group therapy , growth curve , mental health , substance abuse treatment

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 2 • June 2013
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