Sequential medical trials involving paired data

A continuous time version of Anscombe's formulation of the problem of comparing two treatments in the context of medical trials is considered and the Bayes sequential procedure is explicitly determined. Various suboptimal procedures are proposed, evaluated and compared to the optimal procedure; the approximation to the optimal procedure proposed by Anscombe turns out to be surprisingly efficient. Comparison with the discrete time version demonstrates that the continuous time version provides accurate approximations for clinical trials involving horizon sizes as small as 100. The optimal procedure determined here provides a design which is relevant for clinical trials involving either normal or Bernoulli responses. (Author)