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

Owen McGrath; Kevin Burke

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arXiv · 2109.02516

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

Owen McGrath·Kevin Burke

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Abstract

Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald, Clopper-Pearson (exact), Wilson and Agresti-Coull, in the context of rare-event 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 whilst 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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Owen McGrath, Kevin Burke. 2021-09-06. Binomial confidence intervals for rare events: importance of defining margin of error relative to magnitude of proportion. https://arxiv.org/abs/2109.02516

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