Allocation Rules for Sequential Clinical Trials
Consider the following simplified model of a clincial trial. Patients arrive sequentially at a treatment center and receive one of two treatments: A or B. The (immediate response of the ith patient to receive treatment A is xi, i = l,2,..., that of the jth patient to receive treatment B is yj, j = 1,2,.... At any stage of the process, having observed x1,...,xm, y1,...,yn, the experimenter can stop the experiment and declare (1) A is the better treatment, (2) B is better, or (3) there is essentially no difference between A and B; or he can continue the experiment and assign the next patient to treatment A or B according to some allocation rule. In this paper we shall be primarily interested in the experimenter’s allocation rule, which should be selected insofar as possible (i) to permit valid inferences upon termination of the experiment and (ii) to minimize in some sense the number of patients receiving the inferior treatment during the course of the experiment.
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