A Comparison of Methods for Finding the Upper Confidence Limit for a Binomial Proportion When Zero Successes Are Observed

• Activity Number: 344
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Courtney McCracken and Stephen Looney*+
• Companies: Georgia Health Sciences University and Georgia Health Sciences University
• Keywords: Approximate methods ; Binomial parameter ; Exact methods ; P-confidence ; Observed interval length ; Zero successes

Abstract

Confidence interval estimation for a binomial proportion is a long-debated topic, resulting in a wide range of exact and approximate methods. Many of these methods perform quite poorly when the number of observed successes in a sample of size n is zero. In this case, the main objective of the investigator is usually to obtain an upper bound, i.e., the upper limit of a one-sided confidence interval. Traditional notions of expected interval length and coverage probability are not applicable in this situation because it is assumed that the sample data have already been observed. In this presentation we use observed interval length and p-confidence to evaluate eight methods for finding a confidence interval for a binomial proportion when it is known that the number of observed successes is zero. We also consider approximate sample sizes needed to achieve various upper bounds near the zero boundary. We show that many popular approximate methods perform poorly based on these criteria and conclude that the exact method has superior performance in terms of interval length and p-confidence.