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Confidence interval performance is typically assessed in terms of twocriteria: coverage probability and interval width (or margin of error). In thispaper, we assess the performance of four common proportion interval estimators:the Wald, Clopper-Pearson (exact), Wilson and Agresti-Coull, in the context ofrare-event probabilities. We define the interval precision in terms of arelative margin of error which ensures consistency with the magnitude of theproportion. Thus, confidence interval estimators are assessed in terms ofachieving a desired coverage probability whilst simultaneously satisfying thespecified relative margin of error. We illustrate the importance of consideringboth coverage probability and relative margin of error when estimatingrare-event proportions, and show that within this framework, all four intervalestimators perform somewhat similarly for a given sample size and confidencelevel. We identify relative margin of error values that result in satisfactorycoverage whilst being conservative in terms of sample size requirements, andhence suggest a range of values that can be adopted in practice. The proposedrelative margin of error scheme is evaluated analytically, by simulation, andby application to a number of recent studies from the literature.

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