Doubly robust estimation and sensitivity analysis for marginal structural quantile models

TL;DR

This paper introduces a doubly robust estimation method for marginal structural quantile models, enabling causal inference on treatment effects while accounting for model misspecification and unmeasured confounding.

Contribution

It develops a new doubly robust estimator for MSQM, incorporating sensitivity analysis to assess robustness against violations of assumptions.

Findings

Estimator is consistent if either treatment or outcome model is correct.

Estimator achieves semiparametric efficiency when both models are correct.

Simulation studies demonstrate favorable finite-sample performance.

Abstract

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 new doubly robust estimator is proposed for point estimation and inference. 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 semiparametric 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 confounding function approach to investigate the sensitivity of several MSQM estimators when the sequential ignorability assumption is violated. Extensive simulations are conducted to examine the finite-sample performance characteristics of the proposed methods. We apply the proposed methods to the Yale New Haven Health System Electronic Health Record data to study the effect of antihypertensive medications to patients with severe hypertension and assess the robustness of findings to unmeasured baseline and time-varying confounding.