Estimating Moderated Causal Effects with Time-varying Treatments and Time-varying Moderators: Structural Nested Mean Models and Regression with Residuals

Abstract

Individuals differ in how they respond to a particular treatment or exposure, 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 exposure. This article focuses on estimating moderated causal effects in longitudinal settings in which both the treatment and effect moderator vary over time. Effect moderation is typically examined using covariate by treatment interactions in regression analyses, but in the longitudinal setting, this approach may be problematic because time-varying moderators of future treatment may be affected by prior treatment—for example, moderators may also be mediators—and naively conditioning on an outcome of treatment in a conventional regression model can lead to bias. This article introduces to sociology moderated intermediate causal effects and the structural nested mean model for analyzing effect moderation in the longitudinal setting. It discusses problems with conventional regression and presents a new approach to estimation (regression with residuals) that avoids these problems. The method is illustrated using longitudinal data from the Panel Study of Income Dynamics to examine whether the effects of time-varying exposures to poor neighborhoods on the risk for adolescent childbearing are moderated by time-varying family income.