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.

翻译：边际结构分位模型（MSQM）为理解时变处理对潜在结果全分布的影响提供了独特视角。在半参数框架下，我们推导了MSQM的效率影响函数，并据此提出了一种新的双重稳健估计量用于点估计和推断。研究表明，当处理分配模型或潜在结果分布模型任一被正确设定时，该双重稳健估计量具有一致性；当两个模型均正确时，则达到半参数有效性。为实现双重稳健MSQM估计量，我们提出通过求解平滑估计方程来高效计算点估计与方差估计。此外，我们开发了混杂函数方法，用于检验当序贯可忽略性假设被违反时多种MSQM估计量的敏感性。通过大量仿真实验考察了所提方法的有限样本性能，并将该方法应用于耶鲁纽黑文健康系统电子健康记录数据，研究抗高血压药物对严重高血压患者的疗效，同时评估结果对未测量基线与时变混杂的稳健性。