A theory for testing hypotheses under covariate-adaptive randomization

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 un...

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Bibliographic Details
Published in:Biometrika 2010-06, Vol.97 (2), p.347-360
Main Authors: Shao, Jun, Yu, Xinxin, Zhong, Bob
Format: Article
Language:English
Subjects:
Adaptive allocation
Applications
Biased coin
Biology, psychology, social sciences
Bootstrap method
Clinical trial
Clinical trials
Conditional probabilities
Covariance
Estimation bias
Estimators
Exact sciences and technology
General topics
Hypotheses
Hypothesis testing
Inference
Mathematics
Minimization
Modeling
Nonparametric inference
Parametric inference
Power
Probability and statistics
Random allocation
Random variables
Sampling bias
Sciences and techniques of general use
Significance level
Statistical inference
Statistical variance
Statistics
Studies
Type I error
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Summary: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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asq014