OPTIMUM DESIGNS FOR SELECTING ONE OF TWO MEDICAL TREATMENTS SEQUENTIAL PLAN 1

Our present question is how it is possible to design an optimal clinical trial when a total of patients with a disease are to be treated with one of the two medical treatments, where the proportion of the therapeutic efficacy is known for one treatment while unknown for the other. In the planning of medical experiments to asses the therapeutic efficacy of new treatments, a most important question is how large to make the clinical trial. On the one hand, one wants as few patients as possible to participate so that the number of patients receiving the inferior treatment during all of the clinical trial is minimized, the clinical trial is brought to as speedy a conclusion as possible, and the results are quickly made available in the treatment of the many remaining patients with the disease in question. On the other hand, one wants as many patients as possible to participate so that the number of patients receiving the superior treatment during all of the clinical trial is maximized, and enough patients must participate in the clinical trial so that one can be reasonably certain that the truly superior treatment is selected and its subsequent use is appropriate. In the situation of this kind, an application of Neyman-Pearson principle will lose its active meaning. As an alternative, it seems reasonable to approach the problem from the point of view of the consequences of decisions maid, i.e., to use a cost function. Therefore, we should like to introduce the concepts of the expected loss, moreover the overall expected loss (obtained by averaging over an a priori distribution for a parameter). In constructing cost functions the consequences of both right and wrong decisions and the costs of experimentation may be considered. But, from an ethical point of view, the former are the principal concern for us and so we should like to disregard all other costs and concentrate solely on the consequence of treating a patient with the superior or the inferior of the two treatments. In this paper, a sequential plan will be proposed in the case of one sample and discrete type (i.e., binomial type). Namely a clinical trial will