Weighting methods are a common tool to de-bias estimates of causal effects. And though there are an increasing number of seemingly disparate methods, many of them can be folded into one unifying regime: Causal Optimal Transport. This new method directly targets distributional balance by minimizing optimal transport distances between treatment and control groups or, more generally, between a 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 the researcher desires to balance. 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 study examining the effect of misoprostol versus oxytocin for the treatment of post-partum hemorrhage.

翻译：加权方法是降低因果关系估计的常见工具。 虽然似乎有越来越多的不同方法, 但其中许多方法可以被折叠成一个统一的制度: 原因最佳运输。 这种新方法通过最大限度地减少治疗和控制组之间的最佳运输距离,或者更一般地说,减少源与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高效和无模型的,但也可以包含研究者想要平衡的时点或其他重要变量。 我们发现,当偏好性分和结果模型都被错误地描述时, 焦非最佳运输优于竞争方法, 表明这是共同加权方法的有力替代方法。 最后, 我们在一项外部控制研究中展示了我们方法的效用, 研究对产后出血后治疗的厌食醇和氧素的影响。