Journal Article

A theory for testing hypotheses under covariate-adaptive randomization

Jun Shao, Xinxin Yu and Bob Zhong

in Biometrika

Published on behalf of Biometrika Trust

Volume 97, issue 2, pages 347-360
Published in print June 2010 | ISSN: 0006-3444
Published online April 2010 | e-ISSN: 1464-3510 | DOI: https://dx.doi.org/10.1093/biomet/asq014
A theory for testing hypotheses under covariate-adaptive randomization

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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.

Keywords: Adaptive allocation; Biased coin; Clinical trial; Minimization; Power; Type I error

Journal Article.  0 words. 

Subjects: Probability and Statistics

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