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 -