2021/09/06 by Owen McGrath, Kevin Burke, McGrath, Owen +1 · 1 citation
Mathematics · #62F25 #Applications (stat.AP) #FOS: Computer and information sciences #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2109.02516
openalex publication_date 2021/09/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.