配对设计中风险差的置信区间构造  

Confidence interval construction of risk difference in paired design

作　　者：张丽平 古丽斯坦·库尔班尼牙孜 田茂再[1,2] ZHANG Li-Ping;TIAN Mao-Zai(Xinjiang University of Finance and economics,College of Statistics,Urumqi 830012,China;Renmin University of China,School of statistics,Beijing 100872,China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012 [2]中国人民大学统计学院,北京100872

出　　处：《高校应用数学学报（A辑）》2024年第1期28-40,共13页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金)项目(22XNL016)。

摘　　要：风险差在配对设计中常用来对比某种疾病治疗前后或某种政策措施实施前后的有效性.文中针对风险差(Risk Difference)在配对设计中的置信区间估计问题,利用Delta法,改进Wald法,反双曲正切变换法,似然比检验法,鞍点逼近法方法进行置信区间构造,并通过Monte Carlo模拟计算区间覆盖率和区间长度,以比较这5种方法的表现性能.结果显示:不同方法的区间表现均不相同.其中鞍点逼近法明显优于其他4种方法;改进Wald法的表现仅次于鞍点逼近法,且随着样本量的增大,改进Wald法和反双曲正切变换法的性能差距逐渐减小;最后通过一个实例来验证这5种区间估计方法.Risk difference is often used to compare the effectiveness of a disease before and after treatment or the implementation of a policy measure in paired design Aiming at the problem of confidence interval estimation of risk difference in paired design,this paper uses delta method,improved Wald method,inverse hyperbolic tangent transformation method,likelihood ratio test method and saddle point approximation method to construct confidence interval,and calculates the interval coverage and interval length through Monte Carlo simu-lation to compare the performance of thesefive methods.The results show that the interval performance of different methods is different Among them,the saddle point approximation method is significantly better than the other four methods;The performance of the improved Wald method is second only to the saddle point approximation method,and with the increase of the sample size,the performance gap between the improved Wald method and the inverse hyperbolic tangent transformation method gradually decreases;finally an example is given to verify thefive interval estimation methods.

关 键 词：配对设计 鞍点逼近 Monte Carlo模拟 置信区间 

分 类 号：O212.2[理学—概率论与数理统计]