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Abstract:
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Covariate-adjusted response-adaptive (CARA) designs can reduce the number of patients assigned to inferior treatment, as well as balance treatment allocation over important covariates. Since the allocation scheme and the estimation of parameters are based on both responses and covariates, CARA designs are very difficult to formulate and the theoretical properties of conventional hypotheses testing remain unknown. In the literature, most studies are only based on simulations. In this work, we derive the asymptotic distributions of the test statistics for comparing treatment effects under both null and alternative hypotheses. The study is under a simple linear model framework with continuous responses for two treatments. Under a family of CARA designs, the conventional testing is not always valid when omitting some covariates in the inference procedure. Proper adjustment on the variance of test statistic is required to achieve correct Type I error. Numerical studies are performed to verify corresponding finite sample properties.
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