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Type I error and power in trials with one interim futility analysis

Futility analysis reduces the opportunity to commit Type I error. For a superiority study testing a two‐sided hypothesis, an interim futility analysis can substantially reduce the overall Type I error while keeping the overall power relatively intact. In this paper, we quantify the extent of the reduction for both one‐sided and two‐sided futility analysis. We argue that, because of the reduction, we should be allowed to set the significance level for the final analysis at a level higher than the allowable Type I error rate for the study. We propose a method to find the significance level for the final analysis. We illustrate the proposed methodology and show that a design employing a futility analysis can reduce the sample size, and therefore reduce the exposure of patients to unnecessary risk and lower the cost of a clinical trial. Copyright © 2004 John Wiley & Sons, Ltd.