Estimating Post-Treatment Effect Modification With Generalized Structural Mean Models∗

In randomized controlled trials, the evaluation of an overall treatment effect is often followed by effect modification or subgroup analyses, where the possibility of a different magnitude or direction of effect for varying values of a covariate is explored. While studies of effect modification are typically restricted to pretreatment covariates, longitudinal experimental designs permit the examination of treatment effect modification by intermediate outcomes, where intermediates are measured after treatment but before the final outcome. We present a generalized structural mean model (GSMM) for analyzing treatment effect modification by post-treatment covariates. The model can accommodate post-treatment effect modification with both full compliance and noncompliance to assigned treatment status. The methods are evaluated using a simulation study that demonstrates that our approach retains unbiased estimation of effect modification by intermediate variables which are affected by treatment and also predict outcomes. We illustrate the method using a randomized trial designed to promote re-employment through teaching skills to enhance self-esteem and inoculate job seekers against setbacks in the job search process. Our analysis provides some evidence that the intervention was much less successful among subjects that displayed higher levels of depression at intermediate post-treatment waves of the study.