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Sequential rerandomization

Author

Listed:
  • Quan Zhou
  • Philip A Ernst
  • Kari Lock Morgan
  • Donald B Rubin
  • Anru Zhang

Abstract

SummaryThe 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.

Suggested Citation

  • Quan Zhou & Philip A Ernst & Kari Lock Morgan & Donald B Rubin & Anru Zhang, 2018. "Sequential rerandomization," Biometrika, Biometrika Trust, vol. 105(3), pages 745-752.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:745-752.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy031
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    References listed on IDEAS

    as
    1. Kari Lock Morgan & Donald B. Rubin, 2015. "Rerandomization to Balance Tiers of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1412-1421, December.
    2. Xinran Li & Peng Ding, 2017. "General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1759-1769, October.
    3. Zhenzhen Xu & John D. Kalbfleisch, 2013. "Repeated Randomization and Matching in Multi-Arm Trials," Biometrics, The International Biometric Society, vol. 69(4), pages 949-959, December.
    4. Adam Kapelner & Abba Krieger, 2014. "Matching on-the-fly: Sequential allocation with higher power and efficiency," Biometrics, The International Biometric Society, vol. 70(2), pages 378-388, June.
    5. Kosuke Imai & Gary King & Elizabeth A. Stuart, 2008. "Misunderstandings between experimentalists and observationalists about causal inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 481-502, April.
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    1. Hengtao Zhang & Guosheng Yin, 2021. "Response‐adaptive rerandomization," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1281-1298, November.
    2. Yang, Haoyu & Qin, Yichen & Wang, Fan & Li, Yang & Hu, Feifang, 2023. "Balancing covariates in multi-arm trials via adaptive randomization," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Adam Kapelner & Abba Krieger, 2023. "A matching procedure for sequential experiments that iteratively learns which covariates improve power," Biometrics, The International Biometric Society, vol. 79(1), pages 216-229, March.
    4. Ke Zhu & Hanzhong Liu, 2023. "Pair‐switching rerandomization," Biometrics, The International Biometric Society, vol. 79(3), pages 2127-2142, September.
    5. Yves Tillé, 2022. "Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials," International Statistical Review, International Statistical Institute, vol. 90(3), pages 481-498, December.

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