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.

翻译：置信区间性能通常通过两个标准评估：覆盖概率和区间宽度（或误差幅度）。本文在稀有事件概率的背景下，评估了四种常用比例区间估计量的性能：Wald、Clopper-Pearson（精确）、Wilson 和 Agresti-Coull。我们将区间精度定义为相对误差幅度，以确保与比例的大小保持一致。因此，区间估计量的评估依据是：在满足指定相对误差幅度的同时，达到期望的覆盖概率。我们说明了在估计稀有事件比例时，同时考虑覆盖概率和相对误差幅度的重要性，并表明在此框架下，对于给定的样本量和置信水平，所有四种区间估计量的表现大致相似。我们确定了能够实现满意覆盖概率且相对于样本量要求较为保守的相对误差幅度值，从而提出一组可在实践中采用的数值范围。所提出的相对误差幅度方案通过解析方法、模拟以及应用于文献中近期多项研究进行了评估。