Zhou, Quan; Ernst, Philip A.; Morgan, Kari Lock; Rubin, Donald B.; Zhang, Anru Sequential rerandomization. (English) Zbl 1499.62279 Biometrika 105, No. 3, 745-752 (2018). 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. Cited in 11 Documents MSC: 62L05 Sequential statistical design 62K05 Optimal statistical designs 62L10 Sequential statistical analysis Keywords:experimental design; Mahalanobis distance; noncentral chi-squared distribution; sequential enrolment Citations:Zbl 1274.62509 PDFBibTeX XMLCite \textit{Q. Zhou} et al., Biometrika 105, No. 3, 745--752 (2018; Zbl 1499.62279) Full Text: DOI arXiv Link