Sequential Models for Clinical Trials

This paper presents a model, variations of which have been considered by Anscombe 1 and Colton 4 and others, which is relevant to the problem of sequential testing in clinical trials. This model is the same as one discussed by Chernoff and Ray 3 and by Wurtele 7 in a sampling inspection problem and is naturally related to a one armed bandit problem. The object of this paper is to demonstrate that techniques exist for dealing with some of the technical problems raised by these and similar models. A few of the insights derived from the results on the one armed bandit problem will be described in terms of nominal significance levels corresponding to the rejection of a new drug. The model is oversimplified for many practical applications. Alternative models, including a two armed bandit problem are described. An important element in most of these models is the horizon consisting of the total number of anticipated patients to be treated.