Summary The seminal work of Morgan & Rubin (2012) considers rerandomization for all the units at one time.In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result that given the same number of rerandomizations, in expected value, under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.

中文翻译：

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顺序重新随机化

总结 Morgan & Rubin (2012) 的开创性工作考虑一次对所有单元进行重新随机化。然而，在实践中，实验者可能必须按顺序重新随机化单元。例如，研究一种罕见疾病的临床医生可能无法等到所有实验单位都招募完毕后才能进行实验。我们的工作为顺序重新随机化设计提供了一个数学框架，其中实验单元被分组注册。我们制定了一个自适应重新随机化程序，用于在一些连续或二元协变量上平衡治疗/控制分配，使用马哈拉诺比斯距离作为不平衡度量。我们在关键结果中证明，在某些温和的假设下，给定相同数量的重新随机化，在预期值中，