Validity of tests under covariate-adaptive biased coin randomization and generalized linear models

Area of Science:

• Statistics
• Clinical Trials Methodology

Background:

• Covariate-adaptive randomization is used in clinical trials, but theoretical work on hypothesis testing is limited.
• Previous theory focused on linear models; this study extends it to generalized linear models.

Purpose of the Study:

• To establish asymptotic results for covariate-adaptive biased coin randomization under generalized linear models.
• To develop and validate hypothesis testing methods that utilize covariates in randomization.

Main Methods:

• Asymptotic theory for covariate-adaptive biased coin randomization.
• Development of a bootstrap test for hypothesis testing.
• Application to generalized linear models, including binary, Poisson, and exponential distributions.
• Simulation studies to evaluate Type I errors and power.

Main Results:

• The simple t-test is conservative regarding Type I error under covariate-adaptive biased coin randomization.
• A valid bootstrap test is constructed, asymptotically as efficient as Wald's test.
• Covariate-adaptive randomization can recover efficiency lost by not using covariates in analysis.
• An alternative simple test shows validity under covariate-adaptive randomization but inflated Type I error under simple randomization.

Conclusions:

• Covariate-adaptive biased coin randomization offers a valid and efficient approach to hypothesis testing in clinical trials.
• The proposed bootstrap test effectively utilizes covariates, maintaining statistical power.
• Understanding the impact of model misspecification on test validity is crucial.