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A theory for testing hypotheses under covariate-adaptive randomization

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  • Jun Shao
  • Xinxin Yu
  • Bob Zhong

Abstract

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
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    File URL: http://hdl.handle.net/10.1093/biomet/asq014
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. repec:eee:csdana:v:113:y:2017:i:c:p:297-310 is not listed on IDEAS
    5. repec:eee:deveng:v:1:y:2016:i:c:p:12-25 is not listed on IDEAS
    6. 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.

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