Frequentist and Bayesian tolerance intervals for setting specification limits for left-censored gamma distributed drug quality attributes.

IF 1.3 4区 医学 Q4 PHARMACOLOGY & PHARMACY Pharmaceutical Statistics Pub Date : 2024-03-01 Epub Date: 2023-10-23 DOI:10.1002/pst.2344
Richard O Montes
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Abstract

Tolerance intervals from quality attribute measurements are used to establish specification limits for drug products. Some attribute measurements may be below the reporting limits, that is, left-censored data. When data has a long, right-skew tail, a gamma distribution may be applicable. This paper compares maximum likelihood estimation (MLE) and Bayesian methods to estimate shape and scale parameters of censored gamma distributions and to calculate tolerance intervals under varying sample sizes and extents of censoring. The noninformative reference prior and the maximal data information prior (MDIP) are used to compare the impact of prior choice. Metrics used are bias and root mean square error for the parameter estimation and average length and confidence coefficient for the tolerance interval evaluation. It will be shown that Bayesian method using a reference prior overall performs better than MLE for the scenarios evaluated. When sample size is small, the Bayesian method using MDIP yields conservatively too wide tolerance intervals that are unsuitable basis for specification setting. The metrics for all methods worsened with increasing extent of censoring but improved with increasing sample size, as expected. This study demonstrates that although MLE is relatively simple and available in user-friendly statistical software, it falls short in accurately and precisely producing tolerance limits that maintain the stated confidence depending on the scenario. The Bayesian method using noninformative prior, even though computationally intensive and requires considerable statistical programming, produces tolerance limits which are practically useful for specification setting. Real-world examples are provided to illustrate the findings from the simulation study.

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用于设置左删失伽马分布药物质量属性的规格限值的Frequencist和Bayesian容差区间。
质量属性测量的公差区间用于确定药品的规格限制。某些属性测量可能低于报告限制,即左删失数据。当数据具有长的右偏斜尾部时,伽马分布可能适用。本文比较了最大似然估计(MLE)和贝叶斯方法来估计截尾伽玛分布的形状和尺度参数,并计算不同样本量和截尾程度下的容许区间。非形成性参考先验和最大数据信息先验(MDIP)用于比较先验选择的影响。使用的度量是参数估计的偏差和均方根误差,以及公差区间评估的平均长度和置信系数。结果表明,对于所评估的场景,使用参考先验的贝叶斯方法总体上优于MLE。当样本量较小时,使用MDIP的贝叶斯方法保守地产生过宽的公差区间,这不适合作为规范设置的基础。正如预期的那样,所有方法的指标都随着审查程度的增加而恶化,但随着样本量的增加而改善。这项研究表明,尽管MLE在用户友好的统计软件中相对简单且可用,但它在准确、准确地产生保持所述置信度的容限方面存在不足,具体取决于场景。使用非形成先验的贝叶斯方法,即使计算密集且需要大量的统计编程,也会产生对规范设置实际有用的容差极限。提供了真实世界的例子来说明模拟研究的发现。
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来源期刊
Pharmaceutical Statistics
Pharmaceutical Statistics 医学-统计学与概率论
CiteScore
2.70
自引率
6.70%
发文量
90
审稿时长
6-12 weeks
期刊介绍: Pharmaceutical Statistics is an industry-led initiative, tackling real problems in statistical applications. The Journal publishes papers that share experiences in the practical application of statistics within the pharmaceutical industry. It covers all aspects of pharmaceutical statistical applications from discovery, through pre-clinical development, clinical development, post-marketing surveillance, consumer health, production, epidemiology, and health economics. The Journal is both international and multidisciplinary. It includes high quality practical papers, case studies and review papers.
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