Lyles Robert H, Weiss Paul, Waller Lance A
Department of Biostatistics and Bioinformatics, The Rollins School of Public Health of Emory University, 1518 Clifton Rd. N.E., Mailstop 1518-002-3AA, Atlanta, GA 30322.
J Stat Comput Simul. 2020;90(1):75-89. doi: 10.1080/00949655.2019.1672695. Epub 2019 Oct 8.
Drawbacks of traditional approximate (Wald test-based) and exact (Clopper-Pearson) confidence intervals for a binomial proportion are well-recognized. Alternatives include an interval based on inverting the score test, adaptations of exact testing, and Bayesian credible intervals derived from uniform or Jeffreys beta priors. We recommend a new interval intermediate between the Clopper-Pearson and Jeffreys in terms of both width and coverage. Our strategy selects a value κ between 0 and 0.5 based on stipulated coverage criteria over a grid of regions comprising the parameter space, and bases lower and upper limits of a credible interval on (κ, 1- κ) and (1- κ, κ) priors, respectively. The result tends toward the Jeffreys interval if the criterion is to ensure an average overall coverage rate (1-α) across a single region of width 1, and toward the Clopper-Pearson if the goal is to constrain both lower and upper lack of coverage rates at α/2 with region widths approaching zero. We suggest an intermediate target that ensures all average lower and upper lack of coverage rates over a specified set of regions are ≤ α/2. Interval width subject to these criteria is readily optimized computationally, and we demonstrate particular benefits in terms of coverage balance.
二项式比例的传统近似（基于 Wald 检验）和精确（Clopper-Pearson）置信区间的缺点已广为人知。替代方法包括基于对得分检验求逆的区间、精确检验的改编，以及源自均匀或 Jeffreys beta 先验的贝叶斯可信区间。我们推荐一种在宽度和覆盖率方面介于 Clopper-Pearson 和 Jeffreys 区间之间的新区间。我们的策略是根据包含参数空间的区域网格上规定的覆盖标准，在 0 到 0.5 之间选择一个值 κ，并分别基于（κ, 1 - κ）和（1 - κ, κ）先验确定可信区间的下限和上限。如果标准是确保在宽度为 1 的单个区域上的平均总体覆盖率为（1 - α），则结果趋向于 Jeffreys 区间；如果目标是在区域宽度趋近于零时将下限和上限的未覆盖率都限制在 α/2，则结果趋向于 Clopper-Pearson 区间。我们建议一个中间目标，即确保在指定的一组区域上所有平均下限和上限的未覆盖率均≤α/2。符合这些标准的区间宽度很容易通过计算进行优化，并且我们在覆盖平衡方面展示了特别的优势。
