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Binomial confidence intervals for rare events: importance of defining margin of error relative to magnitude of proportion

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posted on 2024-06-07, 09:11 authored by Owen McGrathOwen McGrath, Kevin BurkeKevin Burke

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.

Funding

Confirm Centre for Smart Manufacturing

Science Foundation Ireland

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History

Publication

The American Statistician, pp.1-13

Publisher

Taylor & Francis Group

Department or School

  • Mathematics & Statistics

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