Growth Mixture Modeling for Principal Stratification Analyses: Promises and Caveats

The growth mixture model (GMM) technique has shown promise for principal stratification analyses (Frangakis and Rubin, 2002) in the context of randomized studies. However, due the exploratory nature of GMM (i.e, principal strata are not pre-specified given potential outcomes), more assumptions and/or model constraints could be needed for deriving causal inference compared to the conventional principal stratification technique. The goal of this presentation is to compare the GMM approach proposed by Muthen and Brown (2009) with the hybrid GMM approach by Jo, Wang and Ialongo (2009).  We focus on their difference/similarity in (1) model assumptions required for causal inference (e.g., treatment ignorability, monotonicity, exclusion restriction, or necessary modification that suit GMM); (2) the impact on model estimation associated with model misspecification (e.g., the underlying distribution assumption, the number of classes, or inadequate covariates); and (3) methods for model comparison/diagnostics (e.g., information criteria and residual diagnostics). We will illustrate both these GMM methods in assessing the intervention effect on tobacco use trajectory in a family-centered intervention study in middle school children (Dishion & Kavanagh 2000). Potential benefits of conducting principal stratification analyses by using both the two GMM approaches will be discussed. Due to the data nature in this application example, we will focus on GMM’s with each mixture component assuming a zero-inflated poisson distribution (Nagin 2005), or a 2-part random-effects model (Olsen and Shafer 2001) with the continuous part fit by either a normal or a poisson distribution.