Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this work we assess the performance of four common proportion interval estimators: the Wald, Clopper- Pearson, Wilson and Agresti-Coull, in the context of rare-event probabilities. We define the precision of the interval estimate in terms of a relative margin of error which ensures consistency with the magnitude of the proportion. Thus, confidence interval performance is assessed in terms of achieving a desired coverage probability whilst satisfying the specified relative margin of error. We show that when interval performance is considered using both coverage probability and relative margin of error, 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进行评估：覆盖概率和区间宽度（或误差幅度）。本研究针对稀有事件概率，评估了四种常用比例区间估计量（Wald、Clopper-Pearson、Wilson和Agresti-Coull）的性能。我们定义区间估计的精度为相对误差幅度，该指标确保与比例大小的一致性。因此，置信区间性能的评估标准为：在满足指定相对误差幅度的同时，实现目标覆盖概率。研究表明，当同时使用覆盖概率和相对误差幅度评估区间性能时，四种区间估计量在给定样本量和置信水平下的表现较为相似。我们确定了既能实现满意覆盖概率又能保守控制样本量要求的相对误差幅度值，并据此提出了一组可在实践中采用的取值范围。所提出的相对误差幅度方案通过解析推导、模拟仿真以及文献中多项近期研究的应用实例进行了评估。