Aronow P M, Robins James M, Saarinen Theo, Sävje Fredrik, Sekhon Jasjeet S
Department of Statistics and Data Science Yale University.
Department of Political Science Yale University.
Obs Stud. 2025 Apr 11;11(1):3-16. doi: 10.1353/obs.2025.a956837. eCollection 2025.
We argue that randomized controlled trials (RCTs) are special even among studies for which a nonparametric unconfoundedness assumption is credible. This claim follows from two results of Robins and Ritov (1997). First, in settings with at least one continuous confounder, there exists no estimator of the average treatment effect that is uniformly consistent unless the propensity score is known or additional assumptions are made on the complexity of the propensity score function. Second, with binary outcomes, knowledge of the propensity score yields a uniformly consistent estimator and finite-sample valid confidence intervals that shrink at a parametric rate, regardless of how complicated the propensity score function might be. We emphasize the latter point, and note that a successfully executed RCT provides knowledge of the propensity score to the researcher. We conclude that statistical estimation and inference tend to be fundamentally more difficult in observational settings than in RCTs, even when all confounders are observed and measured without error.
我们认为，即使在非参数无混杂性假设可信的研究中，随机对照试验（RCT）也具有特殊性。这一观点源于罗宾斯和里托夫（1997）的两个结果。首先，在至少存在一个连续混杂因素的情况下，除非倾向得分已知或对倾向得分函数的复杂性做出额外假设，否则不存在一致均匀的平均治疗效果估计量。其次，对于二元结局，无论倾向得分函数多么复杂，倾向得分的知识都会产生一个一致均匀的估计量和以参数速率收缩的有限样本有效置信区间。我们强调后一点，并指出成功实施的RCT会为研究者提供倾向得分的知识。我们得出结论，即使所有混杂因素都被无误差地观察和测量，观察性研究中的统计估计和推断在根本上往往比RCT更困难。
