A bayesian growth mixture model for complex survey data: clustering postdisaster ptsd trajectories

Research on growth mixture models (GMMs) for analyzing data from a complex sample survey is sparse. Existing methods use pseudo-likelihood in which survey weights are incorporated into the likelihood function, with variance estimated via linearization or resampling techniques. Despite popularity of the pseudo-likelihood approach, weighted estimation introduces the risk of efficiency loss. In this paper we propose a Bayesian GMM for complex survey data in which sample design features, such as stratification, clustering, and unequal probability of selection, are incorporated as covariates or hierarchical variance components. The Bayesian GMM can yield a reduction in bias in the estimation of regression coefficients when design features are associated with survey outcomes, and can lead to more efficient estimates than the pseudo-likelihood estimators when the design is noninformative. We develop an efficient Gibbs sampler that includes only closed-form full conditional distributions for model fitting. We present the results of a careful analysis of data from the Galveston Bay Recovery Study (GBRS) which used a stratified multi-stage cluster sample design. Using our proposed Bayesian GMM, we characterize longitudinal trajectories of post-traumatic stress disorder (PTSD) among residents of southeastern Texas in the aftermath of Hurricane Ike. We identify four clinically meaningful PTSD trajectory subgroups and characterize risk factors associated with subgroup membership. In the absence of existing software that can be used to implement our proposed Bayesian GMM for complex survey data, we built the R package Bsvygmm for model fitting, selection, and checking which can be downloaded from https://github.com/anthopolos/Bsvygmm.