Examining Moderated Effects of Additional Adolescent Substance Use Treatment

This article considers the problem of examining causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and putative confounders are time-varying. Robins' (1994) structural nested mean model (SNMM) is used to specify the moderated time-varying causal effects of interest in a conditional mean model for a continuous response given time-varying treatments and candidate time-varying moderators. We present an easy-to-use estimator of the SNMM that combines an existing regression-with-residuals (RR) approach with an inverse-probability-of-treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time-varying causal effects if the candidate time-varying moderators of interest are the sole time-varying confounders. The proposed IPTW+RR approach identifies the moderated time-varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured putative time-varying confounders, which are not candidate time-varying moderators of interest. A small simulation experiment is used to compare IPTW+RR vs the traditional regression approach, and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time-varying moderators and time-varying confounders. The methodology is illustrated in a case study examining the moderated time-varying effects of additional adolescent substance use treatment on future substance use, as a function of time-varying frequency of substance use.