Sequential Medical Trials for Comparing an Experimental with a Standard Treatment

The Bayes sequential solution for a particular formulation of the problem of comparing an experimental with a standard treatment in the context of medical trials is determined. For large horizon size, this solution is represented as the solution of a free-boundary problem which also arises as the solution of a related Wiener-process problem. The nature of the solution of this related problem and the approximation to the medical-trials problem provided by this related problem are examined. Suboptimal procedures are evaluated and one of these, a Wald-type sequential procedure, is found to be surprisingly efficient.