Regression-with-residuals Estimation of Marginal Effects: A Method of Adjusting for Treatment-induced Confounders that may also be Moderators

Abstract: Treatment-induced confounders complicate analyses of time-varying treatment effects and causal mediation. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse-probability-of-treatment-weighted (IPTW) estimation of marginal structural models (MSMs) as well as g- and regression-with-residuals (RWR) estimation of highly constrained structural nested mean models (SNMMs), each suffers from a set of nontrivial limitations. Specifically, IPTW estimation is inefficient, is difficult to use with continuous treatments or mediators, and may suffer from finite-sample bias, while g- and RWR estimation of highly constrained SNMMs for marginal effects are premised on the unrealistic assumption that there is no effect moderation. In this study, we adapt the method of RWR to estimate marginal effects with a set of moderately constrained SNMMs that accommodate several types of treatment-by-confounder and/or mediator-by-confounder interaction, thereby relaxing the assumption of no effect moderation. Through a series of simulation experiments and empirical examples, we show that this approach outperforms IPTW estimation of MSMs as well as both g- and RWR estimation of highly constrained SNMMs in which effect moderation is assumed away.