A class of adaptive sampling schemes for selecting the better of two binomial populations

Abstract

We consider a family of single step allocation methods for the reduction of number of patients given the poorer of two treatments in a sequential comparative clinical trial. The object of the trial is to choose the better treatment with a probability ≧ P^∗, where P^∗ is assigned, when the difference in success probabilities is greater than or equal to an assigned δ^∗. We use the formulation of the trial as a symmetrical selection procedure, Bechhofer, Kiefer, Sobel, 1968, Sobel, Weiss, 1970. If the stopping rule is the difference in successes then either alternating allocation or play the winner allocation appears to be optimal (Robbins, 1956, Sobel, Weiss, 1970.) When the stopping rule takes failures into account alternating allocation is not optimal, and other sirategies become important