Covariate‐adjusted response adaptive designs incorporating covariates with and without treatment interactions

Abstract

AbstractThe covariate‐adjusted response adaptive (CARA) design has been shown to be better than traditional designs in terms of both ethics and efficiency. However, its mechanism for allocating subjects makes certain stochastic processes such as allocated response sequences very complicated. Consequently, the validation of statistical inference is usually challenging, and few theoretical results have been obtained. In this paper we systematically solve some fundamental problems for statistical inference with CARA designs. First, we obtain the conditional independence and distribution of allocated response sequences, which is the basis for further theoretical investigation. Second, we propose a new family of CARA designs, which is extensively applicable. We more importantly provide a framework for new CARA designs with unified asymptotic results for statistical inference. The numerical results demonstrate the advantages of the proposed CARA designs. Our findings are crucial in understanding the CARA design as well as its development and application. The Canadian Journal of Statistics 43: 534–553; 2015 © 2015 Statistical Society of Canada