A kind of multi-treatment adaptive designs with assignment probabilities depending on the estimated parameters∗

The Play-the-Winner (PW) rule is an important method in clinical trials for patient allocation with two treatments, in which the probability a treatment is assigned to the coming patient depends upon the response of the previous patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability a treatment is assigned to the coming patient depends upon both the response of the previous patient and an estimated parameter, say, the estimated success rate. Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments. The strong consistency, the asymptotic normality and the strong approximation are established for the proportion of patients assigned to each treatment. AMS 1999 subject classification. 60F15, 60F05, 62G10, 60G10.