Keywords: Covariate-adjusted response-adaptive designs, Response-adaptive designs, Clinical trials, Generalized linear model, Maximum likelihood, Asymptotic properties
Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well-being of patients and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates which can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate-adjusted response-adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well-being of participating patients. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response-adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well-being of patients under a logit model with categorical covariates. We demonstrate that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.