IDEAS home Printed from
   My bibliography  Save this article

A theory for testing hypotheses under covariate-adaptive randomization


  • Jun Shao
  • Xinxin Yu
  • Bob Zhong


The covariate-adaptive randomization method was proposed for clinical trials long ago but little theoretical work has been done for statistical inference associated with it. Practitioners often apply test procedures available for simple randomization, which is controversial since procedures valid under simple randomization may not be valid under other randomization schemes. In this paper, we provide some theoretical results for testing hypotheses after covariate-adaptive randomization. We show that one way to obtain a valid test procedure is to use a correct model between outcomes and covariates, including those used in randomization. We also show that the simple two sample t-test, without using any covariate, is conservative under covariate-adaptive biased coin randomization in terms of its Type I error, and that a valid bootstrap t-test can be constructed. The powers of several tests are examined theoretically and empirically. Our study provides guidance for applications and sheds light on further research in this area. Copyright 2010, Oxford University Press.

Suggested Citation

  • Jun Shao & Xinxin Yu & Bob Zhong, 2010. "A theory for testing hypotheses under covariate-adaptive randomization," Biometrika, Biometrika Trust, vol. 97(2), pages 347-360.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:347-360

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Antoine Chambaz & Mark J. Laan, 2014. "Inference in Targeted Group-Sequential Covariate-Adjusted Randomized Clinical Trials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 104-140, March.
    2. Atkinson, Anthony C. & Biswas, Atanu, 2017. "Optimal response and covariate-adaptive biased-coin designs for clinical trials with continuous multivariate or longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 297-310.
    3. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2015. "Inference under covariate-adaptive randomization," CeMMAP working papers CWP45/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Guiteras, Raymond P. & Levine, David I. & Polley, Thomas H., 2016. "The pursuit of balance in sequential randomized trials," Development Engineering, Elsevier, vol. 1(C), pages 12-25.
    5. Atkinson, Anthony C. & Biswas, Atanu, 2017. "Optimal response and covariate-adaptive biased-coin designs for clinical trials with continuous multivariate or longitudinal responses," LSE Research Online Documents on Economics 66761, London School of Economics and Political Science, LSE Library.
    6. Jun Shao & Xinxin Yu, 2013. "Validity of Tests under Covariate-Adaptive Biased Coin Randomization and Generalized Linear Models," Biometrics, The International Biometric Society, vol. 69(4), pages 960-969, December.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:347-360. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.