两阶段设计中单比例的精确置信区间构造  

On Construction of Exact Confidence Interval for the Proportion in Two-Stage Designs

作　　者：尹环 王维真 YIN Huan;WANGWei-zhen(School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China;Department of Mathematics and Statistics,Wright State University,Dayton 45435,USA)

机构地区：[1]华北电力大学数理学院,北京102206 [2]Department of Mathematics and Statistics,Wright State University,Dayton 45435,USA

出　　处：《数理统计与管理》2024年第6期1053-1064,共12页Journal of Applied Statistics and Management

基　　金：国家自然科学基金资助项目(12101233);北京市自然科学基金资助项目(1222002)。

摘　　要：在Ⅱ期临床试验中药物疗效不确定的情况下,通常要求参与试验的人数尽可能少。二项分布下单比例的估计多使用基于大样本的渐近区间。Ⅱ期临床试验中大样本一般得不到,因此希望给出参数的精确置信区间,即极小覆盖概率不低于1-α。在两阶段优化设计背景下,本文将依据Clopper-Pearson区间和反搜索法给出原始样本空间上的一个合理秩函数,并在该秩函数下构造最优的精确单侧置信区间。从在整个参数空间上的覆盖概率图可以看出,该置信区间的置信系数不低于1-α。进一步,以期望区间长度为评价标准,将提出的新区间与两个已知的精确区间进行比较,发现新区间期望长度更短。最后以乳腺癌药物-奥拉帕尼的数据(2018年3月至2020年1月)为例,给出该药物疗效率的最优精确下单侧置信区间。In Phase Ⅱ clinical trials,when the eficacy of a drug is uncertain,the number of participants is often expected to be as small as possible.The commonly used confidence intervals of the single proportion of binomial distribution are the results of the large sample theory.However,for small samples,due to the inapplicability of large samples,we prefer to give exact confidence intervals of the parameter,that is,the minimum coverage probability is not less than 1-α.In this paper,the rank function on the original sample space is constructed based on the Clopper-Pearson interval and inverse search methods,and an optimal exact confidence interval is derived under this order in two-stage designs.By depicting the coverage probability graph on the whole parameter space,it can be seen that the confidence coeffcient of the interval is not less than 1-Q.Further,taking the expected interval length as the evaluation standard,we compare three exact intervals,and the expected length of the new interval is the shortest in general.Finally,the data of olaparib(2018.03-2020.01),a breast cancer drug,is used to derive the optimal exact lower one-sided confidence interval for the efficacy rate of olaparib.

关 键 词：二项分布 Ⅱ期临床试验 期望区间长度 秩函数 置信系数 

分 类 号：O212[理学—概率论与数理统计]