Sequential medical trials involving paired data

Abstract

A general approach to sequential decision-theoretic problems is illustrated with Anscombe's formulation of the problem of comparing two treatments in a medical trial. The Bayes sequential procedure for a continuous time verion of the problem is explicitly determined. Suboptimal procedures are proposed and evaluated; asymptotic results and numerical descriptions are provided. The continuous time version is found to provide accurate approximations even for clinical trials involving relatively small horizon sizes.