Covariate Adjustment in Randomized Experiments Motivated by Higher-Order Influence Functions
受高阶影响函数启发的随机实验协变量调整AI 解读 ↓
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受高阶影响函数启发的随机实验协变量调整
- 研究问题
- 随机试验中基线协变量数量相对样本量较大时，如何改进处理组特定均值的调整估计，并判断它何时优于未经调整的均值估计？
- 方法与思路
- 作者构造受高阶影响函数启发的协变量调整估计量，分析其与常用调整及未调整方法的统计性质，并将若干近期方法纳入统一解释框架。
- 材料陈述的贡献
- 摘要称，高维协变量情形下所提估计量改善常用调整方法的统计性质，并刻画优于未调整估计的条件，辅以数值和实证研究。
- 阅读关注点
- 应核对改善针对偏差、方差还是其他准则，协变量维数与样本量的关系，以及随机化方案、工作模型、推断有效性和统一表示的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核验；摘要未列出改善条件、具体统计界或实验数值，不能把结果理解为任意维数下均更好。
原文摘要
Higher-Order Influence Functions (HOIF), developed in a series of papers over the past twenty years, are a fundamental theoretical device for constructing rate-optimal causal-effect estimators from observational studies. However, the value of HOIF for analyzing well-conducted randomized controlled trials (RCT) has not been explicitly explored. In the recent U.S. Food and Drug Administration and European Medicines Agency guidelines on the practice of covariate adjustment in analyzing RCT, in addition to the simple, unadjusted difference-in-mean estimator, it was also recommended to report the estimator adjusting for baseline covariates via a simple parametric working model, such as a linear model. However, when the number of baseline covariates $p$ is large, the recommendation is somewhat murky. In this paper, we show that HOIF-motivated estimators for the treatment-specific mean have significantly improved statistical properties compared to popular adjusted estimators in practice when $p$ is relatively large relative to the sample size $n$. We also characterize the conditions under which the HOIF-motivated estimator improves upon the unadjusted one. More importantly, we demonstrate that several state-of-the-art adjusted estimators proposed recently can be interpreted as particular HOIF-motivated estimators, thereby placing these estimators in a more unified framework. Numerical and empirical studies are conducted to corroborate our theoretical findings. An accompanying R package can be found on CRAN.