Some covariate-adaptive randomization methods have been used in clinical trials for a long time, but little theoretical work has been done about testing hypotheses under covariate-adaptive randomization until Shao et al. (2010) who provided a theory with detailed discussion for responses under linear models. In this article, we establish some asymptotic results for covariate-adaptive biased coin randomization under generalized linear models with possibly unknown link functions. We show that the simple t-test without using any covariate is conservative under covariate-adaptive biased coin randomization in terms of its Type I error rate, and that a valid test using the bootstrap can be constructed. This bootstrap test, utilizing covariates in the randomization scheme, is shown to be asymptotically as efficient as Wald's test correctly using covariates in the analysis. Thus, the efficiency loss due to not using covariates in the analysis can be recovered by utilizing covariates in covariate-adaptive biased coin randomization. Our theory is illustrated with two most popular types of discrete outcomes, binary responses and event counts under the Poisson model, and exponentially distributed continuous responses. We also show that an alternative simple test without using any covariate under the Poisson model has an inflated Type I error rate under simple randomization, but is valid under covariate-adaptive biased coin randomization. Effects on the validity of tests due to model misspecification is also discussed. Simulation studies about the Type I errors and powers of several tests are presented for both discrete and continuous responses.
Covariate-adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate-adaptive randomization is limited to tests under linear or generalized linear models, although the covariate-adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate-adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate-adaptive randomization. We also show that the unstratified log-rank test is conservative and the stratified log-rank test remains valid under covariate-adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate-adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log-rank-type tests in terms of Pitman’s asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.
more » « less- NSF-PAR ID:
- 10398636
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 82
- Issue:
- 5
- ISSN:
- 1369-7412
- Format(s):
- Medium: X Size: p. 1301-1323
- Size(s):
- ["p. 1301-1323"]
- Sponsoring Org:
- National Science Foundation
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