Using Structural Nested Mean Models to Examine Time-varying Moderators of the Effect of Substance Use Treatment
*Daniel Almirall, University of Michigan 
Beth Ann Griffin, RAND  
Daniel F. McCaffrey, RAND 
Susan A. Murphy, University of Michigan, Dept of Statistics 
Rajeev Ramchand, RAND 

Keywords: substance abuse treatment, time-varying moderation, 2-stage regression, time-varying confounding, structural nested mean models, incremental causal effects

Most analyses examining moderated effects of treatment focus on moderation by time-invariant characteristics of patients measured at baseline/intake. However, most clients in substance abuse treatment experience multiple treatment episodes over time, and the putative moderators of interest may also be time-varying. In this talk, we discuss Robins' Structural Nested Mean Model (SNMM) for examining time-varying causal effect moderation. We describe an easy-to-use 2-stage regression estimator for the intermediate causal effects of the SNMM; and we introduce an extension of the 2-stage regression estimator that is useful when there exist many more time-varying confounders than time-varying moderators of interest. We illustrate the methodology using a large, observational study data set of adolescent substance users receiving outpatient and/or residential treatment. In the analysis, we examine the incremental causal effects of additional treatment as a function of improvements or decline over time.