  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.

Methodology