An optimal response adaptive biased coin design with k heteroscedastic treatments

For comparing treatments in clinical trials, Atkinson (1982) introduced optimal biased coins for balancing patients across treatment assignments by using D-optimality under the assumption of homoscedastic responses of different treatments. However, this assumption can be violated in many real applications. In this paper, we relax the homoscedasticity assumption in the k   treatments setting with k>2k>2. A general family of optimal response adaptive biased coin designs are proposed following Atkinson's procedure. Asymptotic properties of the proposed designs are obtained. Some advantages of the proposed design are discussed.