Doubly robust estimation and sensitivity analysis for marginal structural quantile models
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The marginal structure quantile model (MSQM) is a useful tool to characterize the causal effect of a time-varying treatment on the full distribution of potential outcomes. However, to date, only the inverse probability weighting (IPW) approach has been developed to identify the structural causal parameters in MSQM, which requires correct specification of the propensity score models for the treatment assignment mechanism. We propose a doubly robust approach for the MSQM under the semiparametric framework. We derive the efficient influence function associated with a MSQM and estimate causal parameters in the MSQM by combining IPW and a new iterative conditional regression approach that models the full potential outcome distribution. The proposed approach is consistent if either of the models associated with treatment assignment or the potential outcome distributions is correctly specified, and is locally efficient if both models are correct. To implement the doubly robust MSQM estimator, we propose to solve a smoothed estimating equation to facilitate efficient computation of the point and variance estimates. In addition, we develop a new confounding function and sensitivity analysis strategy to investigate the robustness of several MSQM estimators when the no unmeasured confounding assumption is violated. We apply the proposed methods to the Yale New Haven Health System Electronic Health Record data to study the causal effect of antihypertensive medications to inpatients with severe hypertension, and assess the robustness of findings to unmeasured time-varying confounding.
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