No star is good news: A unified look at rerandomization based on $p$-values from covariate balance tests
没有显著星号是好消息：基于协变量平衡检验 p 值的再随机化AI 解读 ↓
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没有显著星号是好消息：基于协变量平衡检验 p 值的再随机化
- 研究问题
- 按协变量平衡检验的 p 值筛选随机分配后，平均处理效应的常用回归估计量会如何变化，标准推断是否仍然有效？
- 方法与思路
- 作者研究多种基于 p 值的再随机化方案，分别推导未调整、加性调整及完全交互回归估计量的渐近抽样性质。
- 材料陈述的贡献
- 摘要称完全交互回归在所考察方案中渐近最有效率；再随机化也提高另两类估计量效率，而常规回归推断可能过于保守。
- 阅读关注点
- 核对再随机化的接受规则、渐近条件和效率比较范围，并检查完全交互回归采用的标准误与有限样本推断表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；结论限于所研究方案和渐近框架，摘要未说明有限样本保证及具体条件。
原文摘要
Modern social and biomedical scientific publications require the reporting of covariate balance tables with not only covariate means by treatment group but also the associated $p$-values from significance tests of their differences. The practical need to avoid small $p$-values renders balance check and rerandomization by hypothesis testing standards an attractive tool for improving covariate balance in randomized experiments. Despite the intuitiveness of such practice and its arguably already widespread use in reality, the existing literature knows little about its implications on subsequent inference, subjecting many effectively rerandomized experiments to possibly inefficient analyses. To fill this gap, we examine a variety of potentially useful schemes for rerandomization based on $p$-values (ReP) from covariate balance tests, and demonstrate their impact on subsequent inference. Specifically, we focus on three estimators of the average treatment effect from the unadjusted, additive, and fully interacted linear regressions of the outcome on treatment, respectively, and derive their respective asymptotic sampling properties under ReP. The main findings are twofold. First, the estimator from the fully interacted regression is asymptotically the most efficient under all ReP schemes examined, and permits convenient regression-assisted inference identical to that under complete randomization. Second, ReP improves not only covariate balance but also the efficiency of the estimators from the unadjusted and additive regressions asymptotically. The standard regression analysis, in consequence, is still valid but can be overly conservative.