Regression‐with‐residuals estimation of marginal effects: a method of adjusting for treatment‐induced confounders that may also be effect modifiers

When making causal inferences, treatment‐induced confounders complicate analyses of time‐varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between the treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse probability of treatment weighted estimation of marginal structural models as well as g‐ and regression‐with‐residuals estimation of highly constrained structural nested mean models, each suffers from a set of non‐trivial limitations, among them an inability to accommodate effect modification. In this study, we adapt the method of regression with residuals to estimate marginal effects with a set of moderately constrained structural nested mean models that easily accommodate several types of treatment‐by‐confounder interaction. With this approach, the confounders at each time point are first residualized with respect to the observed past, which involves centring them at their estimated means given prior treatments and confounders. The outcome is then regressed on all prior variables, including a set of treatment‐by‐confounder interaction terms, with these residuals substituted for the untransformed confounders both as ‘main effects’ and as part of any interaction terms. Through a series of simulation experiments and empirical examples, we show that this approach outperforms other methods for estimating the marginal effects of time‐varying treatments.