Asymptotic Properties of Covariate - Adjusted Adaptive Designs

Owing to the benefits that higher proportions of patients are likely to receive the better treatment, response-adaptive designs are considered to be valuable statistical tools in clinical studies. Nevertheless, there is a lack of a comprehensive study of adaptive designs with the inclusion of covariates, regardless of their importance in clinical experiments. The major reason is that covariateadjusted adaptive designs are extreme complex to formulate. For covariateadjusted adaptive designs, both the allocation scheme and the estimation of parameters are being affected not only by the responses, but also by the covariates. In this paper, we have overcome the technical hurdles and layout the framework of the general covariate-adjusted adaptive design for the allocation of subjects to K(≥ 2) treatments. This design can be applied to different types of responses. The asymptotic properties and the advantages of this general adaptive design are studied under some widely satisfied conditions. Two important special cases, linear model and logistic regression model, are considered in details. For comparing two treatments with binary responses, we find that the covariate-adjusted design allocates more subjects to the better treatment at each given covariate level, and the overall success proportion is higher than treatment allocation schemes without incorporating covariates.