Abstract

Double-blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this estimator is unbiased over all possible randomizations does not, however, mean that any given estimate is close to the true treatment effect. Similarly, while predetermined covariates will be balanced between treatment and control groups on average, large imbalances may be observed in a given experiment and the researcher may therefore want to condition on such covariates using linear regression. This article studies the theoretical properties of both the difference-in-means and OLS estimators conditional on observed differences in covariates. By deriving the statistical properties of the conditional estimators, we can establish guidance for how to deal with covariate imbalances.

摘要

双盲随机对照试验传统上被视为因果推断的黄金标准，因为均值差异估计量是实验中平均治疗效果的无偏估计量。然而，该估计量对所有可能的随机化无偏这一事实并不意味着任何给定的估计都接近真实的治疗效果。类似地，虽然预先确定的协变量将平均在治疗组和对照组之间得到平衡，但在给定的实验中可能会观察到很大的不平衡，因此研究人员可能希望使用线性回归来调整这些协变量。本文研究了均值差和 OLS 估计量条件的理论性质关于观察到的协变量差异。通过推导条件估计量的统计特性，我们可以为如何处理协变量不平衡建立指导。