Two-Step Growth Mixture Modeling As a Practical Tool for Longitudinal Causal Inference

Statistical analyses that identify heterogeneous outcome trajectories and trajectory-specific intervention effects may hold important treatment implications and useful information for future intervention trials. Growth mixture modeling (GMM) helps to identify subpopulations that develop into heterogeneous trajectory strata, as well as to identify heterogeneous intervention effects for these strata in the context of intervention/treatment studies. The advantage of GMM is that it can identify both trajectory strata and strata specific treatment effects simultaneously based on empirical model fitting (1-step approach: Jo, 2012; Muthén et al., 2002; Muthén & Brown, 2009). Its heavy reliance on empirical model fitting and parametric assumptions is at the same a major drawback of this approach. In this paper, we will examine the possibilities of using a 2-step GMM approach (Jo, Wang, & Ialongo, 2009) as a practical tool for causal inference in the context of longitudinal intervention studies. In the 2-step hybrid GMM approach, empirical fitting plays a critical role in identifying trajectory strata (step 1), but not necessarily in identifying strata-specific intervention effects (step-2). Once we agree on the trajectory strata solution under a reference condition (e.g., control) in step-1, we may attempt to identify strata-specific treatment effects in step-2. In step-2, we treat the estimated trajectory strata membership as known for the control and missing for the treatment group individuals. How we identify strata-specific causal intervention effects resembles that of principal stratification (Frangakis & Rubin, 2002). The difference is, however, that we utilize rich information from longitudinal intervention contexts and designs. In particular, this paper focuses on a randomized intervention trial setting, where outcome is repeatedly measured over time after a short intervention period. This 2-step approach opens up possibilities of incorporating identification and sensitivity analysis strategies that depend less on empirical fitting and parametric assumptions. We will examine various possibilities of identifying strata-specific intervention effects by combining the strengths of GMM and principal stratification approaches. Based on Monte Carlo simulations and analytic approaches, we will examine conditions under which this 2-step approach is likely to successfully identify causal intervention effects for substantively or clinically meaningful trajectory strata. Longitudinal development of behavioral and substance use problems among children from the Johns Hopkins School Intervention Trial will be presented as an example. It is shown that heterogeneous trajectory types benefit quite differently from the universal intervention program.