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Sequential rerandomization. (English) Zbl 1499.62279

Summary: The seminal work of K. L. Morgan and D. B. Rubin [Ann. Stat. 40, No. 2, 1263–1282 (2012; Zbl 1274.62509)] 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.

MSC:

62L05 Sequential statistical design
62K05 Optimal statistical designs
62L10 Sequential statistical analysis

Citations:

Zbl 1274.62509
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