Residual Balancing Weights for Marginal Structural Models: with Application to Analyses of Time-varying Treatments and Causal Mediation
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Treatment-induced confounding arises in analyses of time-varying treatments and also causal mediation where post-treatment variables affect both the mediator and outcome. In such settings, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of exposure to treatment and/or a mediator and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, susceptible to finite-sample bias, and difficult to use with continuous exposures. 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 treatment-induced confounders rather than the conditional distributions of exposure to treatment and/or a mediator, and it is therefore easier to use with continuous exposures. Using numeric simulations, we show that residual balancing is both more efficient and more robust to model misspecification compared with IPW and its variants. We illustrate the method by estimating (a) the cumulative effect of negative advertising on election outcomes and (b) the controlled direct effect of exposure to an impoverished neighborhood on child academic achievement while controlling for classroom size in a child's school. Open source software is available for implementing the proposed method.
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