Abstract

In comparative studies, balancing influential baseline covariates is fun

damental to the credible assessment of treatment effects.

Two prominent design strategies are covariate-adaptive randomization (CAR) and rerandomiza-

tion (RR). CAR is typically used in clinical trials in which subjects are enrolled

sequentially, whereas RR is formulated for settings in which all subjects are

randomized simultaneously. Although both approaches aim to reduce covariate

imbalance, their mechanisms differ substantially, which has hindered systematic comparisons between them. This article develops a unified framework for

rigorously comparing CAR and RR. We show that RR can match the balance

properties of CAR only under increasingly stringent acceptance thresholds. We

also study the implications of these thresholds for treatment-effect estimation

and for the computational burden of RR. Under such stringent thresholds, the

computational cost of RR grows polynomially with sample size but exponentially

with feature dimension. Consequently, while RR can effectively balance covariates in small to moderate studies, its computational cost escalates rapidly as the

sample size and feature dimension increase, limiting its scalability in large trials. In contrast, CAR remains computationally efficient while delivering strong

balance guarantees under both sequential and simultaneous enrollment settings.

These results clarify the theoretical properties of CAR and RR and provide new

insights into their relative merits for the design of randomized controlled trials.

Key words and phrases: Covariate-adaptive randomization; Rerandomization; Covariate imbalance; Treatment effect estimation; Computational cost

Information

Preprint No.SS-2025-0493
Manuscript IDSS-2025-0493
Complete AuthorsZiji Qin, Feifang Hu, Yang Liu
Corresponding AuthorsYang Liu
Emailsyangliu2022@ruc.edu.cn

References

  1. Athey, S. and G. W. Imbens (2017). The econometrics of randomized experiments. In Handbook of Economic Field Experiments, Volume 1, pp. 73–140. Amsterdam: Elsevier.
  2. Baldi Antognini, A. and M. Zagoraiou (2011). The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika 98(3), 519–535.
  3. Bruce, C. L., E. Juszczak, R. Ogollah, C. Partlett, and A. Montgomery (2022). A systematic review of randomisation method use in rcts and association of trial design characteristics with method selection. BMC Medical Research Methodology 22(1), 314.
  4. Brune, L., E. Chyn, and J. Kerwin (2021). Pay me later: Savings constraints and the demand for deferred payments. American Economic Review 111(7), 2179–2212.
  5. Efron, B. (1971). Forcing a sequential experiment to be balanced. Biometrika 58(3), 403–417.
  6. Hu, F., X. Ye, and L.-X. Zhang (2023). Multi-arm covariate-adaptive randomization. Science China Mathematics 66(1), 163–190.
  7. Hu, Y. and F. Hu (2012). Asymptotic properties of covariate-adaptive randomization. The Annals of Statistics 40(3), 1794–1815.
  8. Johansson, P., D. B. Rubin, and M. Schultzberg (2021). On optimal rerandomization designs. Journal of the Royal Statistical Society Series B: Statistical Methodology 83(2), 395–403.
  9. Johansson, P. and M. Schultzberg (2022). Rerandomization: A complement or substitute for stratification in randomized experiments? Journal of Statistical Planning and Inference 218, 43–58.
  10. Kahan, B. C., A. B. Forbes, C. J. Dor´es, and T. P. Morris (2015). A re-randomisation design for clinical trials. BMC Medical Research Methodology 15(1), 96.
  11. Keller, M. B., J. P. McCullough, D. N. Klein, et al. (2000). A comparison of nefazodone, the cognitive behavioral-analysis system of psychotherapy, and their combination for the treatment of chronic depression. New England Journal of Medicine 342(20), 1462–1470.
  12. Li, X. and P. Ding (2020). Rerandomization and regression adjustment. Journal of the Royal Statistical Society Series B: Statistical Methodology 82(1), 241–268.
  13. Li, X., P. Ding, and D. B. Rubin (2018). Asymptotic theory of rerandomization in treatment– control experiments. Proceedings of the National Academy of Sciences 115(37), 9157–9162.
  14. Liu, Y. and F. Hu (2022). Balancing unobserved covariates with covariate-adaptive randomized experiments. Journal of the American Statistical Association 117(538), 875–886.
  15. Liu, Y. and F. Hu (2023). The impacts of unobserved covariates on covariate-adaptive randomized experiments. The Annals of Statistics 51(5), 1895–1920.
  16. Liu, Y., Y. Zhou, P. Li, and F. Hu (2022). Adaptive a/b test on networks with cluster structures. In International Conference on Artificial Intelligence and Statistics, pp. 10836– 10851. PMLR.
  17. Liu, Y., Y. Zhou, P. Li, and F. Hu (2024). Cluster-adaptive network a/b testing: From randomization to estimation. Journal of Machine Learning Research 25(170), 1–48.
  18. Ma, W., F. Hu, and L. Zhang (2015). Testing hypotheses of covariate-adaptive randomized clinical trials. Journal of the American Statistical Association 110(510), 669–680.
  19. Ma, W., P. Li, L.-X. Zhang, and F. Hu (2024). A new and unified family of covariate adaptive randomization procedures and their properties. Journal of the American Statistical Association 119(545), 151–162.
  20. Ma, W., Y. Qin, Y. Li, and F. Hu (2020). Statistical inference for covariate-adaptive randomization procedures. Journal of the American Statistical Association 115(531), 1488–1497.
  21. Meyn, S. P. and R. L. Tweedie (2013). Markov Chains and Stochastic Stability (3rd ed.).
  22. Cambridge, United Kingdom: Cambridge University Press.
  23. Morgan, K. L., D. B. Rubin, et al. (2012). Rerandomization to improve covariate balance in experiments. The Annals of Statistics 40(2), 1263–1282.
  24. Owen, S. (2023). College major choice and beliefs about relative performance: An experimental intervention to understand gender gaps in stem. Economics of Education Review 97, 102479.
  25. Pocock, S. J. and R. Simon (1975). Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 31(1), 103–115.
  26. Qin, Y., Y. Li, W. Ma, H. Yang, and F. Hu (2024). Adaptive randomization via mahalanobis distance. Statistica Sinica 34, 353–375.
  27. Rosenberger, W. F., O. Sverdlov, et al. (2008). Handling covariates in the design of clinical trials. Statistical Science 23(3), 404–419.
  28. Shao, J., X. Yu, and B. Zhong (2010). A theory for testing hypotheses under covariate-adaptive randomization. Biometrika 97(2), 347–360.
  29. Taves, D. R. (1974). Minimization: a new method of assigning patients to treatment and control groups. Clinical Pharmacology & Therapeutics 15(5), 443–453.
  30. Wang, X., T. Wang, and H. Liu (2023). Rerandomization in stratified randomized experiments. Journal of the American Statistical Association 118(542), 1295–1304.
  31. Wang, Y. and X. Li (2022). Rerandomization with diminishing covariate imbalance and diverging number of covariates. The Annals of Statistics 50(6), 3439–3465.
  32. Yang, H., Y. Qin, F. Wang, Y. Li, and F. Hu (2023). Balancing covariates in multi-arm trials via adaptive randomization. Computational Statistics & Data Analysis 179, 107642.
  33. Zhou, Q., P. A. Ernst, K. L. Morgan, D. B. Rubin, and A. Zhang (2018). Sequential rerandomization. Biometrika 105(3), 745–752. Ziji Qin

Acknowledgments

The authors would like to thank the editor, AE, and the two reviewers for

the insightful comments. Liu’s research was supported by the Fundamental

Research Funds for the Central Universities and the Research Funds of

University of China [grant no. 202630333].

Supplementary Materials

The Supplementary Materials contain proofs of the theoretical results

and additional simulation results.

Supplementary materials are available for download.