An Alternate Method to Find the Confidence Interval for the Difference Between Two Proportions of Rare Event

• Activity Number: 29 - Statistical Issues Specific to Therapeutic Areas, Power and Sample Size Calculations, and Trial Monitoring
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Ruji Yao* and Amarjot Kaur and qing li
• Companies: Merck & Co., Inc. and Merck & Co., Inc. and Merck & co., Inc.
• Keywords: only binomial assumption; Clopper-Pearson; Miettinen, O. and Nurminen, M; confidence interval; rare event rate; posterior distribution

Abstract

In a clinical trial, it is common to have an adverse event summary table to show the difference of event rates and their 95% confidence intervals (CI). The Miettinen, O. and Nurminen, M (M&N) [1] method is often used for this summary. When dealing with a difference of rare events, one possible concern is the normality assumption. In this presentation, we propose a new method for obtaining the CI, which is sometimes more suitable for computing the difference of two proportions of rare event. First, we will use the formula of Exact (Clopper-Pearson) [2] Confidence Limits to define the posterior distributions on observed data. This help us to avoid the need to pick up a Beta (a,b) prior in a Bayesian method. We then calculate the confidence interval directly from these posterior distributions without making a normality assumption for the critical values. Most importantly, our method only makes use of the binomial assumption on the observed data. Compared with the M&N method, we find that our method has very similar results when the differences of rates are in the normal range, but a much narrower widths for the CI when considering differences between rare events.