Sample size recalculation for binary data in internal pilot study designs

Abstract

For binary endpoints, the required sample size depends not only on the known values of significance level, power and clinically relevant difference but also on the overall event rate. However, the overall event rate may vary considerably between studies and, as a consequence, the assumptions made in the planning phase on this nuisance parameter are to a great extent uncertain. The internal pilot study design is an appealing strategy to deal with this problem. Here, the overall event probability is estimated during the ongoing trial based on the pooled data of both treatment groups and, if necessary, the sample size is adjusted accordingly. From a regulatory viewpoint, besides preserving blindness it is required that eventual consequences for the Type I error rate should be explained. We present analytical computations of the actual Type I error rate for the internal pilot study design with binary endpoints and compare them with the actual level of the chi‐square test for the fixed sample size design. A method is given that permits control of the specified significance level for the chi‐square test under blinded sample size recalculation. Furthermore, the properties of the procedure with respect to power and expected sample size are assessed. Throughout the paper, both the situation of equal sample size per group and unequal allocation ratio are considered. The method is illustrated with application to a clinical trial in depression. Copyright © 2004 John Wiley & Sons Ltd.