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.

翻译：边际结构量化模型(MSQM)提供了一个独特的透镜,以了解时间分配处理对潜在结果的全面分布的因果关系。 在半参数框架内,我们从中得出MSQM的效率影响功能,从中提出一个双倍强的估算符。我们表明,如果与治疗分配或潜在结果分布有关的模型中任何一个得到正确指定,那么双倍强的估算符是一致的,如果两种模型都正确,则半对数效率是半数的。我们还开发了一个新的敏感度分析框架,用于假设没有不测的时间变化的混和。