Zou Yixuan, Young Derek S
Department of Statistics, University of Kentucky, Lexington, Kentucky, USA.
Stat Med. 2020 Jul 20;39(16):2152-2166. doi: 10.1002/sim.8537. Epub 2020 Apr 6.
Statistical tolerance intervals are commonly employed in biomedical and pharmaceutical research, such as in lifetime analysis, the assessment of biosimilarity of branded and generic versions of biopharmaceutical drugs, and in quality control of drug products to ensure that a specified proportion of the products are covered within established acceptance limits. Exact two-sided parametric tolerance intervals are only available for the normal distribution, while exact one-sided parametric tolerance limits are available for a limited number of distributions. Approximations to two-sided parametric tolerance intervals often use the Bonferroni correction on the one-sided tolerance interval calculation; however, this often incurs a higher coverage probability than the nominal level. Recently, the usage of a bootstrap calibration has been demonstrated as a way to improve coverage probabilities of tolerance intervals for very specific and complex distributional settings. We present a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals. Simulation results clearly demonstrate the improved coverage probabilities towards the nominal level over the uncalibrated setting. Applications to medical data for various parametric distributions also highlight the utility of constructing these calibrated tolerance intervals.
统计容忍区间常用于生物医学和制药研究，例如在寿命分析、生物制药品牌药和仿制药的生物相似性评估以及药品质量控制中，以确保在既定的验收限度内涵盖指定比例的产品。精确的双边参数容忍区间仅适用于正态分布，而精确的单边参数容忍限度仅适用于有限数量的分布。双边参数容忍区间的近似值通常在单边容忍区间计算中使用邦费罗尼校正；然而，这通常会导致覆盖概率高于标称水平。最近，已证明使用自助校准是一种在非常特殊和复杂的分布设置下提高容忍区间覆盖概率的方法。我们重点介绍使用单层自助校准来提高双边参数容忍区间的覆盖概率。模拟结果清楚地表明，与未校准设置相比，覆盖概率朝着标称水平有所提高。将其应用于各种参数分布的医学数据也突出了构建这些校准容忍区间的实用性。
