负二项抽样下需处理数置信区间构造方法的改进  

IMPROVED CONFIDENCE INTERVAL FOR THE NUMBER NEEDED TO TREAT UNDER NEGATIVE BINOMIAL SAMPLING

作　　者：舒焕[1,2] 封达道[1,2] 田茂再[1,2] 

机构地区：[1]中国人民大学应用统计科学研究中心,北京100872 [2]中国人民大学统计学院,北京100872

出　　处：《系统科学与数学》2012年第9期1047-1056,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11271368);教育部人文社会重点研究基地重大项目(08JJD910247);教育部科学技术研究重点项目(108120);北京市哲学社会科学规划项目(12JGB051);中国人民大学科学研究基金项目(10XNK025),中国人民大学科学研究基金项目(重大基础研究计划)(10XNL018);全国统计科研计划项目(2011LZ031)资助课题

摘　　要：负二项抽样因其在发病率很低的情况下的优良表现而被广泛应用于流行病学及其它学科之中."需处理数"是一种度量药物疗效的重要指标,它常常用来评价那些结果是二值变量的临床试验所研究的药物的疗效.在实际应用中,通常希望得到需处理数的置信区间,但是目前已有的需处理数的置信区间构造方法都存在一个应用上的难题:区间上限过大以至于不可靠.文章旨在解决需处理数区间上限估计过大的问题,为此提出了需处理数的最短区间构造方法并运用蒙特卡洛模拟方法比较其相对传统方法的优劣,还给出了实际应用的例子.模拟结果表明:改进后的方法能够在控制置信系数的情况下极大地减小区间上限,具有重要的实际价值.Negative binomial sampling are wildy used in epidemiology and many other fields owing to its good performance in binary results clinical trails when the prevalence of the disease is rare. As a measurement of drug effect of randomized controlled trials with binary outcomes, the number needed to treat （NNT） is a useful way of reporting trials results. In clinical appliction, we prefer to report the confidence interval of the number needed to treat. The most popular confidence interval for a number needed to treat is the Wald type interval. Unfortunately, the upper confidence limit of Wald type interval often trends to be unreliable. In this paper, the shortest interval is proposed as an improved confidence interval for the number need to be treat which can reduce the upper confidence limit of the interval. Monte Calro Simulation method is used to compare the perfromance of the improved interval with the Wald type interval, and two illustratvie examples show that the improved interval has a coverage probablity close to the confidence coefficient 95% and can reduce the upper confidence limit of interval significantly, which is of practical importance.

关 键 词：需处理数 Wald区间 最短区间 蒙特卡洛模拟 负二项抽样 

分 类 号：O212.2[理学—概率论与数理统计]