基于梯度统计量的逆抽样下风险差的置信区间构建

Confidence Interval Construction Based on Gradient Statistics for Rsik Difference Under Sapling

通过逆抽样过程获得的分布又称为负二项分布,在流行病学研究和二分类变量分布的研究中应用极为广泛。因此,提出两种基于梯度统计量的逆抽样下风险差的置信区间的构建方法,分别依据风险差的极大似然估计(MLE)和方差最小无偏一致估计量(UMVUE)。与现有的WALD方法和得分方法相比,该方法所构建置信区间的优点在于:置信区间构建方法既不需要计算Fisher信息阵也不需要计算其逆矩阵,可使计算得以大大简化;对所提出的基于梯度统计量的置信区间构建方法进行蒙特卡洛模拟研究,模拟结果表明提出的构建方法可以得到很好的覆盖概率和较短的区间宽度。

In epidemiology study , inverse sampling , w hich is also know n as negative binomial sampling ,is a common sampling scheme .In this paper ,for the construction of the confidence interval for risk difference under inverse sampling ,we develop two gradient statistics based methods ,which depend on the maximum likelihood estimator （MLE） and uniformly minimum variance unbiased estimator （UMVUE） respectively .Differently from the WALD and SCORE based methods ,our proposed methods do not need to compute the Fisher information matrix nor its inverse .Simulations are carried out to compare with the likelihood ratio and Score test based methods .We illustrate our proposed methods with a real data set from a drug comparison study .Our results further confirm previous findings .