Abstract：
In epidemiology and social sciences, propensity score methods are popular for estimating treatment effects using observational data, and multiple imputation is popular for handling covariate missingness. However, how to appropriately use multiple imputation for propensity score analysis is not completely clear. This paper aims to bring clarity on the consistency (or lack thereof) of methods that have been proposed, focusing on the within approach (where the effect is estimated separately in each imputed dataset and then the multiple estimates are combined) and the across approach (where typically propensity scores are averaged across imputed datasets before being used for effect estimation). We show that the within method is valid and can be used with any causal effect estimator that is consistent in the full-data setting. Existing across methods are inconsistent, but a different across method that averages the inverse probability weights across imputed datasets is consistent for propensity score weighting. We also comment on methods that rely on imputing a function of the missing covariate rather than the covariate itself, including imputation of the propensity score and of the probability weight. Based on consistency results and practical flexibility, we recommend generally using the standard within method. Throughout, we provide intuition to make the results meaningful to the broad audience of applied researchers.
摘要：
在流行病学和社会科学中，倾向评分方法在使用观察数据估计治疗效果方面很流行，多重插补在处理协变量错误时很受欢迎。然而,如何恰当地使用多重归因进行倾向评分分析尚不完全清楚。本文旨在澄清已提出的方法的一致性(或缺乏一致性)，重点关注内部方法（在每个估算数据集中分别估计效果，然后合并多个估计）和跨方法（通常在用于效果估计之前，在估算数据集中平均倾向得分）。我们证明了内部方法是有效的，并且可以与在完整数据设置中一致的任何因果效应估计器一起使用。现有的跨方法是不一致的，但是不同的方法平均估计数据集的逆概率权重对于倾向得分加权是一致的。我们还评论了依赖于估算缺失协变量而不是协变量本身的函数的方法，包括倾向得分和概率权重的估算。基于一致性结果和实际灵活性，我们建议一般使用标准内方法。在整个过程中,我们提供直觉，使结果对广大应用研究人员有意义。
