Asymptotic Efficiency of A Sequential Allocation Rule

In a clinical trial of two treatments, one goal of the experimenter is to design an experiment such that the number of patients assigned to the inferior treatment is minimized. A Bayesian formulation for this problem is studied. Treatment outcomes are assumed to be indepencL•mt and normally distributed, with conjugate priors. The analysis is conducted in a large sample limit where sampling costs are scaled to zero. First we show there is little harm in restricting attention to procedures that stop according to Kiefer and Sacks stopping rule. There are procedures in this class with risks that exceed the minimum Bayes risk by the cost of a fixed number of observations. Using this we then develop fully efficient procedures with risks asymptotic to the minimum Bayes risk in our large sample limit. A Monte Carlo study indicates that these procedures perform better than the pairwise procedure.