TY - JOUR

T1 - Binomial Confidence Intervals for Rare Events

T2 - Importance of Defining Margin of Error Relative to Magnitude of Proportion

AU - McGrath, Owen

AU - Burke, Kevin

N1 - Publisher Copyright:
© 2024 The Author(s). Published with license by Taylor & Francis Group, LLC.

PY - 2024

Y1 - 2024

N2 - 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-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 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.

AB - 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-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 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.

KW - Binomial

KW - Confidence interval

KW - Coverage

KW - Margin of error

KW - Proportion

KW - Rare event

UR - http://www.scopus.com/inward/record.url?scp=85194288017&partnerID=8YFLogxK

U2 - 10.1080/00031305.2024.2350445

DO - 10.1080/00031305.2024.2350445

M3 - Article

AN - SCOPUS:85194288017

SN - 0003-1305

VL - 78

SP - 437

EP - 449

JO - American Statistician

JF - American Statistician

IS - 4

ER -