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.

翻译：现代社会科学与生物医学出版物要求报告协变量平衡表，不仅需包含按处理组划分的协变量均值，还需附带其差异显著性检验的p值。为避免出现小p值的实际需求，使得基于假设检验标准的平衡检验与再随机化成为改善随机化实验中协变量平衡的有力工具。尽管此类实践具有直观性且已在现实中被广泛应用，但现有文献对其后续推断的影响知之甚少，导致许多实际已执行再随机化的实验可能采用低效的分析方法。为填补这一空白，本文考察了基于协变量平衡检验p值的再随机化（ReP）多种潜在有效方案，并论证其对后续推断的影响。具体而言，我们聚焦于三种平均处理效应估计量——分别来自未调整、加法项及完全交互项的线性回归（以结果变量对处理变量进行回归），并推导它们在ReP下的渐进抽样性质。主要发现有两方面：第一，在考察的所有ReP方案中，完全交互项回归的估计量渐进效率最高，且允许与完全随机化下相同的便捷回归辅助推断；第二，ReP不仅改善了协变量平衡，还从渐进角度提升了未调整回归与加法项回归估计量的效率。因此，标准回归分析虽仍有效，但可能过于保守。