Shan Guogen, Lou XiangYang, Wu Samuel S
Department of Biostatistics, University of Florida, Gainesville, FL 32610.
J Stat Theory Appl. 2023 Jun;22(1-2):38-53. doi: 10.1007/s44199-023-00054-8. Epub 2023 Apr 1.
Confidence interval for the difference of two proportions has been studied for decades. Many methods were developed to improve the approximation of the limiting distribution of test statistics, such as the profile likelihood method, the score method, and the Wilson method. For the Wilson interval developed by Beal (1987), the approximation of the Z test statistic to the standard normal distribution may be further improved by utilizing the continuity correction, in the observation of anti-conservative intervals from the Wilson interval. We theoretically prove that the Wilson interval is nested in the continuity corrected Wilson interval under mild conditions. We compare the continuity corrected Wilson interval with the commonly used methods with regards to coverage probability, interval width, and mean squared error of coverage probability. The proposed interval has good performance in many configurations. An example from a Phase II cancer trial is used to illustrate the application of these methods.
两个比例之差的置信区间已经研究了数十年。人们开发了许多方法来改进检验统计量极限分布的近似,比如轮廓似然法、计分法和威尔逊法。对于比尔(1987年)提出的威尔逊区间,在观察到威尔逊区间存在反保守区间的情况下,通过使用连续性校正可以进一步改善Z检验统计量对标准正态分布的近似。我们从理论上证明,在温和条件下,威尔逊区间嵌套于连续性校正后的威尔逊区间。我们就覆盖概率、区间宽度和覆盖概率的均方误差,将连续性校正后的威尔逊区间与常用方法进行了比较。所提出的区间在许多情况下都具有良好的性能。通过一个II期癌症试验的例子来说明这些方法的应用。
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