Covariate-adjusted response-adaptive designs for generalized linear models

• Theorems of CARA designs for generalized linear models are given.
• Our method allows the absence of some treatment-by-covariate interactions.
• Asymptotic allocation proportions and failure rates are studied.
• The logistic regression model is used for illustrative purpose.
• A simulation study is conducted to evaluate the proposed designs.

Response-adaptive designs have been shown to be useful in reducing the expected number of patients receiving inferior treatments in clinical trials. Zhang et al. (2007) developed a framework for covariate-adjusted response-adaptive designs that can be applied to the class of generalized linear models, providing treatment allocation strategies and estimation methods. However, their results are based on a full model in which all treatment-by-covariate interactions are present. Without relevant distribution theorems on the estimation of parameters in a reduced model, the testing of hypotheses regarding main effects, covariate effects, or their intersections is impossible with their framework. In this paper, we address this deficiency and develop the necessary theoretical properties to conduct hypothesis testing. The theorems that we develop are applicable to generalized linear models. To assist with the comprehension of our proposed framework, we apply it to the logistic regression model for illustrative purposes. We also discuss a procedure for producing asymptotic expected failure rates and treatment proportions, an area neglected in previous covariate-adjusted response-adaptive design research. A simulation study is also presented to reveal the operational characteristics of the framework, including the treatment allocations, failure rates, and test power for various covariate-adjusted response-adaptive designs.