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Binomial confidence intervals for rare events: importance of defining margin of error relative to magnitude of proportion
Date
Abstract
Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this article, we assess the performance of four common proportion interval estimators: the Wald, Clopper-Pearson (exact), Wilson and Agresti-Coull, in the context of rare-bevent probabilities. We define the interval precision in terms of a relative margin of error which ensures consistency with the magnitude of the proportion. Thus, confidence interval estimators are assessed in terms of achieving a desired coverage probability whilst simultaneously satisfying the specified relative margin of error. We illustrate the importance of considering both coverage probability and relative margin of error when estimating rare-event proportions, and show that within this framework, all four interval estimators perform somewhat similarly for a given sample size and confidence level. We identify relative margin of error values that result in satisfactory coverage while being conservative in terms of sample size requirements, and hence suggest a range of values that can be adopted in practice. The proposed relative margin of error scheme is evaluated analytically, by simulation, and by application to a number of recent studies from the literature.
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Description
Publisher
Taylor & Francis Group
Citation
The American Statistician, pp.1-13
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McGrath_2024_Binomial.pdf
Adobe PDF, 1.8 MB
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Funding Information
Sustainable Development Goals
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Type
Article
Rights
https://creativecommons.org/licenses/by-nc-sa/4.0/