Submitted to the Annals of Statistics ASYMPTOTIC PROPERTIES OF COVARIATE-ADJUSTED RESPONSE-ADAPTIVE DESIGNS

Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their im-portance in clinical experiments. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the tech-nical hurdles and lay out a framework for general CARA designs for the allocation of subjects to K( ≥ 2) treatments. The asymptotic properties are studied under certain widely satisfied conditions. The proposed CARA designs can be applied to generalized linear mod-els. Two important special cases, the linear model and the logistic regression model, are considered in detail. 1. Preliminaries. 1.1. Brief history. In most clinical trials, patients accrue sequentially. Response-adaptive designs provide allocation schemes that assign different treatments to incoming patients based on the previous observed responses of patients. A ma-jor objective of response-adaptive designs in clinical trials is to minimize the number of patients that is assigned to the inferior treatment to a degree that still generates useful statistical inferences. The ethical and other characteristics of response-adaptive designs have been extensively discussed by many authors (e.g., Zelen and Wei (1995))