Exact Repeated Confidence Intervals for Bernoulli Parameters in a Group Sequential Clinical Trial Paul R. Coe, Ph.D. and Ajit C. Tamhane, Ph.D. Roosevelt University, Chicago, Illinois (P.R.C.) and Northwestern University, Evanston, Illinois (A. C. T.) ABSTRACT: This paper presents methods for constructing exact repeated confidence intervals (RCIs) for the success probability, p, of a single Bernoulli treatment and for the dif- ference of success probabilities, a = pl - p2, of two independent Bernoulli treatments in the context of a group sequential clinical trial. These RCIs calculated at each interim analysis are useful for evaluating the data in light of all the information available rather than relying on rigid stopping criteria used by repeated significance tests. Extensions to construction of RCIs for the relative risk p = pl/p2 and odds ratio 0~ = pffl - p2)/ p2(1 - pl) are indicated. KEY WORDS: Repeated confidence intervals, interim analyses, binomial distribution, Berkson's simple difference, relative risk, odds ratio INTRODUCTION In order to detect early evidence of treatment differences or harmful side ef- fects, periodic reviews of the accumulating data (called interim analyses) are often performed in clinical trials. Many sequential methods have been devel- oped for this purpose, most taking the form of a repeated significance test. These methods have not been readily embraced in practice, however, because the rigid stopping criteria that they require are often inappropriate in clinical settings [1,2]. More appropriate in these settings is the use of repeated confidence in- tervals (RCIs), which allow the study results to be evaluated flexibly at each review in light of all the information available including the data on efficacy, safety, and concurrent findings of other research groups [3]. RCIs were first derived independently by Lai [4] and Jennison and Turnbull [5] for normally distributed responses. These authors also indicated how the large sample normal approximation theory can be used to derive RCIs for the parameters of interest in problems involving nonnormal data such as Bernoulli and survival. For a recent review of the work on this topic, see an article by Jennison and Turnbull [6]. Address reprint requests to: Prof. Ajit C. Tamhane, Department of Statistics, Northwestern University, 2006 Sheridan Road, Evanston, Illinois 60208-4070. Received September 27, 1991; revised August 13, 1992. Controlled Clinical Trials 14:19-29 (1993) 19 © Elsevier Science Publishing Co., Inc. 1993 0197-2456/93/$6.00 655 Avenue of the Americas, New York, New York 10010