Two-sample binary phase 2 trials with low type I error and low sample size

We address design of two-stage clinical trials comparing experimental and control patients. Our end point is success or failure, however measured, with null hypothesis that the chance of success in both arms is p₀ and alternative that it is p₀ among controls and p₁  > p₀ among experimental patients. Standard rules will have the null hypothesis rejected when the number of successes in the (E)xperimental arm, E, sufficiently exceeds C, that among (C)ontrols. Here, we combine one-sample rejection decision rules, E⩾m, with two-sample rules of the form E - C > r to achieve two-sample tests with low sample number and low type I error. We find designs with sample numbers not far from the minimum possible using standard two-sample rules, but with type I error of 5% rather than 15% or 20% associated with them, and of equal power. This level of type I error is achieved locally, near the stated null, and increases to 15% or 20% when the null is significantly higher than specified. We increase the attractiveness of these designs to patients by using 2:1 randomization. Examples of the application of this new design covering both high and low success rates under the null hypothesis are provided. Copyright © 2017 John Wiley & Sons, Ltd.