基于频率统计和贝叶斯统计的零事件率区间估计方法比较研究  

Comparative Study on the Interval Estimation of Zero Event Proportion based on Frequentist and Bayesian Statistics

作　　者：刘晋 Tianxin Shi 赵杨 邵方 Liu Jin;Tianxin Shi;Zhao Yang(Clinical Medicine Research Institution,The First Affiliated Hospital of Nanjing Medical University,210029,Nanjing)

机构地区：[1]南京医科大学第一附属医院临床研究院,210029 [2]College of liberal arts,University of Minnesota Twin Cities,Minneapolis,USA [3]南京医科大学公共卫生学院生物统计学系

出　　处：《中国卫生统计》2023年第1期15-19,26,共6页Chinese Journal of Health Statistics

基　　金：国家自然科学基金青年基金(81602938)。

摘　　要：目的零事件率是当抽样事件数为零时二项率的一种特殊情形,对其区间估计缺乏深入研究。方法利用二项分布和贝塔分布的关系,使用SAS 9.8设计三层嵌套9.4亿个参数空间点的计算密集型模拟实验,从区间精度、准确度和基于精确法的相对误差三个方面比较了三种频率方法和两种贝叶斯方法区间估计的统计性能,并通过医学实例说明其应用。结果首次报告了在保证覆盖率满足名义水平的条件下,精确法优于Wilson近似法的临界样本量。在平衡估计精度(区间宽度)和估计准确度(覆盖率)的思想指导下,通过大规模统计模拟和实例分析,推荐使用精确法进行零事件率的区间估计。结论随着医学技术的进步,零事件率越来越多地出现在医学研究中,在对这一特殊率进行统计推断时,推荐使用精确法。Objective Zero event proportion is a special case of binomial proportion when the number of sampling events is zero.Due to the limitation of study methods,there is a lack of in-depth and systematic study on it.Methods Based on the relationship between Binomial and Beta distribution,a computationally intensive simulation experiment with three-level nesting of 940 million parameter space points was designed using SAS 9.8.The statistical performance of the interval estimation of three frequentist methods and two Bayesian methods is compared in terms of interval precision,accuracy and relative error based on Exact method,and its application is illustrated with medical examples.Results It is reported for the first time that the critical sample size of the Exact method is superior to the Wilson approximation method under the condition that the coverage probability meets the nominal level.After balancing the interval width and coverage,through large-scale statistical simulation and case analysis,it is recommended to use the Exact method to estimate the interval of zero event proportion.Conclusion With the progress of medical technology,the zero event is more and more appearing in medical research,and it is recommended to use the Exact method when making statistical inference on this special case.

关 键 词：零事件率 频率统计 贝叶斯统计 区间估计 

分 类 号：R195.1[医药卫生—卫生统计学]