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Using randomization tests to preserve type I error with response adaptive and covariate adaptive randomization

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  • Simon, Richard
  • Simon, Noah Robin

Abstract

We demonstrate that clinical trials using response adaptive randomized treatment assignment rules are subject to substantial bias if there are time trends in unknown prognostic factors and standard methods of analysis are used. We develop a general class of randomization tests based on generating the null distribution of a general test statistic by repeating the adaptive randomized treatment assignment rule holding fixed the sequence of outcome values and covariate vectors actually observed in the trial. We develop broad conditions on the adaptive randomization method and the stochastic mechanism by which outcomes and covariate vectors are sampled that ensure that the type I error is controlled at the level of the randomization test. These conditions ensure that the use of the randomization test protects the type I error against time trends that are independent of the treatment assignments. Under some conditions in which the prognosis of future patients is determined by knowledge of the current randomization weights, the type I error is not strictly protected. We show that response adaptive randomization can result in substantial reduction in statistical power when the type I error is preserved. Our results also ensure that type I error is controlled at the level of the randomization test for adaptive stratification designs used for balancing covariates.

Suggested Citation

  • Simon, Richard & Simon, Noah Robin, 2011. "Using randomization tests to preserve type I error with response adaptive and covariate adaptive randomization," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 767-772, July.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:767-772
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    Citations

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    Cited by:

    1. Helen Yvette Barnett & Sofía S. Villar & Helena Geys & Thomas Jaki, 2023. "A novel statistical test for treatment differences in clinical trials using a response‐adaptive forward‐looking Gittins Index Rule," Biometrics, The International Biometric Society, vol. 79(1), pages 86-97, March.
    2. Michael A. Proschan, 2021. "Discussion on “Improving precision and power in randomized trials for COVID‐19 treatments using covariate adjustment for binary, ordinal, and time‐to‐event outcomes”," Biometrics, The International Biometric Society, vol. 77(4), pages 1482-1484, December.
    3. Ting Ye & Jun Shao, 2020. "Robust tests for treatment effect in survival analysis under covariate‐adaptive randomization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1301-1323, December.

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