Incorporating auxiliary variables to improve efficiency of time-varying treatment effect estimation
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we present a method for improving causal effect estimation using auxiliary variables, which extends baseline covariate adjustment results beyond single-time-point treatment to time-varying treatment. Existing results concerning asymptotic precision of causal effects are established in the context of randomized controlled trials (RCTs), and it has been demonstrated that covariate adjustment improves or does not hurt asymptotic precision, even when the regression model is incorrect. However, it is still unclear how these covariate adjustment approaches will work with data arising from contexts where treatments, responses, and moderators are time-varying, such as in an MRT. To fill this knowledge gap, we propose a general method called “A2-WCLS”” for auxiliary variable adjusted WCLS with data from MRTs. Under mild conditions, it provides a consistent and asymptotically normal estimate of the moderated causal excursion effect, while retaining or improving estimation efficiency.Through simulation studies and analysis of data from the Intern Health Study, the efficiency gain of the proposed method is demonstrated in comparison to the benchmark WCLS method