Sequential rerandomization

Quan Zhou, Philip A. Ernst, Kari Lock Morgan, Donald B. Rubin, Anru Zhang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)745-752
Number of pages8
Issue number3
StatePublished - Sep 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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