Bayes Rules for a Clinical-Trials Model with Dichotomous Responses

Abstract

The risk in a trial to compare two medical treatments is borne by the patients who receive the inferior treatment during the experimental phase and by those remaining after the experiment who will all receive the inferior treatment if the results are misleading. The Bayes rule indicates, for the observed progression of successes and failures, when it is optimal to stop this experimental phase. This stopping rule can be described exactly, or nearly so, for symmetric two-point priots. Less precise descriptions are possible for other types of priors. An admissible stopping rule is described which is best possible, among symmetric Bayes rules, in that it minimizes the probability of choosing the inferior treatment no matter what the values are for the probabilities of success.