Estimating Heterogeneous Causal Effects with Time-Varying Treatments and Time-Varying Effect Moderators: Structural Nested Mean Models and Regression-with-Residuals

Geoffrey T. Wodtke, University of Toronto
Daniel Almirall, University of Michigan

Individuals differ in how they respond to a particular treatment, and social scientists are often interested in understanding how treatment effects are moderated by observed characteristics of individuals. Effect moderation occurs when individual covariates dampen or amplify the effect of some treatment. This article focuses on conceptualizing and estimating moderated causal effects in longitudinal settings where both the treatment and effect moderator of interest vary over time. Effect moderation is typically examined using covariate-by-treatment interactions in conventional regression analyses, but in the longitudinal setting, this approach is problematic because time-varying moderators of future treatment may be affected by prior treatment (i.e., moderators may also be mediators). Conditioning on a mediator of prior treatment in a conventional regression model leads to bias from over-control of intermediate pathways and collider stratification. This article introduces moderated intermediate causal effects and the structural nested mean model for analyzing effect heterogeneity in the longitudinal setting.