  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.
