Conditional Confidence Intervals for p1-p2 and p1/p2 Using a Generalized Fisher's Exact Test

• Activity Number: 65
• Type: Contributed
• Date/Time: Sunday, July 29, 2007 : 4:00 PM to 5:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Devan V. Mehrotra and Arthur Roth*+
• Companies: Merck & Co., Inc. and Pfizer Inc.
• Keywords: nuisance parameter ; confidence interval ; Fisher's exact test ; difference of proportions ; ratio of proportions

Abstract

Fisher's exact test compares two independent binomial proportions, p1 and p2, using conditional inference. It can be viewed as a test on the odds ratio OR=[p1/(1-p1)]/[p2/(1-p2)], the difference D=p1-p2, or the ratio R=p1/p2, i.e., the null hypothesis can be written as OR=1, D=0, or R=1. A corresponding exact conditional confidence interval (CI) to complement the p-value from Fisher's test is easy to construct for OR based on a natural ancillary statistic, but not for D or R, which have no ancillary statistics, making it necessary to deal with a nuisance parameter. We propose two solutions to the nuisance parameter dilemma, each within the context of a "generalized Fisher's exact" (GFE) test. Illustrative examples and exact numerical results are provided to demonstrate the superiority of our GFE-based conditional CIs for D and R relative those proposed by Santner and Snell (JASA, 1980).