Residual Balancing: A Method of Constructing Weights for Marginal Structural Models

When making causal inferences, post-treatment 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 treatment and the outcome, leading to bias. To avoid such bias, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of treatment and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, susceptible to finite-sample bias, and difficult to use with continuous treatments. We introduce an alternative method of constructing weights for MSMs, which we call “residual balancing”. In contrast to IPW, it requires modeling the conditional means of the post-treatment confounders rather than the conditional distributions of treatment, and it is therefore easier to use with continuous treatments. Numeric simulations suggest that residual balancing is both more efficient and more robust to model misspecification than IPW and its variants in a variety of scenarios. We illustrate the method by estimating (a) the cumulative effect of negative advertising on election outcomes and (b) the controlled direct effect of shared democracy on public support for war. Open-source software is available for implementing the proposed method.