Modified Bayes technique in sequential clinical trials

We consider the problem of optimizing the treatment of a population by two drugs of unknown efficacy. The success or failure of each treatment is assumed to be known before the next patient arrives to be treated, and the objective is to use the developing information both to select optimally for a given patient and to asymptotically restrict treatment to the better of the two drugs. A straightforward Bayes estimator is first assumed. It is shown by computer simulation, and to some extent algebraically, that this leads to the possibility of "trapping" into treatment by the poorer drug, due to early anomalously poor performance by the better drug. The difficulty is ameliorated by imposing a bias towards success on the input (a priori) distribution of the unknown success probabilities. In fact, the resulting protocol, which is ethical from the point of view of the individual patient, is also superior for the full treated population to a few sampling-plus-stopping-rule techniques against which it is compared.