Several papers recently have discussed the design of clinical trials from a gain function viewpoint (Anscombe 1963, Colton 1963, 1965, and, on a very similar topic, Wetherill and Campling 1966 among others). This paper considers the situation in which two treatments are available for a particular ailment. The response to the treatment is a continuous variable, and the gain in using a treatment is some monotonic function of the value of the response. A given number N of patients will be in need of one or other of the two treatments, and the trial is aimed at allocating the treatments to the patients in such a way as to make the expected gain as large as possible. The trial which achieves the largest expected gain is of considerable complexity, involving a decision with each patient as to which treatment to use, and usually one confines attention to trials with a simpler design. Colton 1963 considered single-stage designs and sequential probability ratio tests, and in a later paper 1965 two types of two-stage designs. In this paper, less restricted and unrestricted two-stage designs are constructed and evaluated. The model used here is the same as used by Colton, and is as follows:
N. E. Day (1969) studied this question.