for Certain Clinical Trials

Suppose that two treatments are available for use in a clinical trial. Further suppose that the response to treatment is either positive (a success) or negative (a failure) and that the patients can be treated one at a time, with each patient's response available before the next patient is to be treated. The number of patients in the trial is N, which may be fixed or random; the latter possibility will be discussed in Section 6. The objective of the trial is to maximize the number of positive responses from these N patients. An inevitable and obviously beneficial result of any trial is the acquisition of information concerning the treatments. This accumulating information allows for better treatment of patients appearing late in the trial than those appearing early. The treatment allocation problem for early phases of the trial is then governed by two possibly conflicting considerations: (1) A patient should be given the treatment which is apparently superior; (2) A patient should be given the treatment about which more is likely to be learned. Denote the probability of success using treatment 1 by pi and using treatment 2 by P2. If pi and P2 are known precisely then there is no information to be collected during the course of the trial, and the best plan for the trial is to allocate all to the treatment which has the larger pi, and for that allocation the expected number of