Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational studies. This leaves researchers to choose the proper weighting method and the appropriate covariate functions for these models without knowing the correct combination to achieve distributional balance. In response to these difficulties, we propose a nonparametric generalization of several other weighting schemes found in the literature: Causal Optimal Transport. This new method directly targets distributional balance by minimizing optimal transport distances between treatment and control groups or, more generally, between any source and target population. Our approach is semiparametrically efficient and model-free but can also incorporate moments or any other important functions of covariates that a researcher desires to balance. Moreover, our method can provide nonparametric estimate the conditional mean outcome function and we give rates for the convergence of this estimator. Moreover, we show how this method can provide nonparametric imputations of the missing potential outcomes and give rates of convergence for this estimator. We find that Causal Optimal Transport outperforms competitor methods when both the propensity score and outcome models are misspecified, indicating it is a robust alternative to common weighting methods. Finally, we demonstrate the utility of our method in an external control trial examining the effect of misoprostol versus oxytocin for the treatment of post-partum hemorrhage.
翻译:孔径分布的不平衡导致对因果关系的偏差估计。 加权方法试图纠正这种不平衡,但依靠指定治疗分配机制的模式,这是观察研究中未知的。 这使得研究人员可以在不知道正确组合的情况下选择这些模型的适当加权方法和适当的共差功能,而不知道实现分配平衡的正确组合。 针对这些困难,我们建议对文献中的其他若干加权办法进行非对称的概括化: causal Optimal Transport。 这一新方法通过尽量减少治疗和控制组之间或更一般地说来任何源和目标人群之间的最佳运输距离,直接针对分配平衡。 我们的方法是半对称有效和无型的处理机制。 我们的方法可以包含研究者想要平衡的共变体的瞬间或任何其他重要功能。 此外,我们的方法可以提供非对等值估计条件平均结果的计算率,我们为这个估计器的合并率提供了一种非对称性的潜在结果,并为这个估量器提供了非对称的处理率。 我们发现,在选择的顶端和直径分析结果的方法中, Causor Obrial Oprial train 方法是一种常态分析结果。