Doubly robust estimation and sensitivity analysis for marginal structural quantile models

The marginal structure quantile model (MSQM) provides a unique lens to understand the causal effect of a time-varying treatment on the full distribution of potential outcomes. Under the semiparametric framework, we derive the efficiency influence function for the MSQM, from which a doubly robust estimator is proposed. We show that the doubly robust estimator is consistent if either of the models associated with treatment assignment or the potential outcome distributions is correctly specified, and is semiparametrically efficient if both models are correct. We also develop a novel sensitivity analysis framework for the assumption of no unmeasured time-varying confounding.