Resumen de On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling

Elliott Nebenzahl

• Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability = P*, where P* is assigned, when the difference in success probabilities is = ?*, ?* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if the stopping rule is based on the difference in successes then either alternating allocation or play-the-winner allocation appears to be optimal (Robbins, 1956; Sobel, Weiss, 1970). We make precise the above statement and then in our main theorem prove it to be true for all ?* sufficiently small and P* ? 1