基于鞍点逼近的二项抽样下优势比的置信区间构造

发布时间：2019-03-24 18:53

【摘要】：优势比通常用来分析疾病与暴露因素的关联强度,在医学研究中有非常重要的临床意义。对于优势比而言,得到其一个区间估计往往比得到一个点估计更加重要。实际数据分析中,优势比作为一个未知参数其估计量比较复杂,要得到其精确的分布是很难实现的,因此一般都寻求其一个渐近的置信区间。文中,我们采用四种方法来构造二项抽样下优势比的渐近置信区间,分别为Delta方法、Woolf方法、基于似然比检验的方法以及鞍点逼近方法,每种方法都各有其优缺点,其中鞍点逼近方法构造优势比的置信区间,是本文的一个创新点。我们通过蒙特卡洛模拟来比较这四种区间估计方法的优劣,对于模拟结果的评价准则主要基于区间对优势比真值的覆盖率与置信水平的接近程度和平均区间长度这两个指标。最后,本文通过两个实证案例来直观展示四种区间估计方法的不同特点。
[Abstract]:Advantage ratio is usually used to analyze the intensity of association between disease and exposure factors, which is of great clinical significance in medical research. As far as the advantage ratio is concerned, it is more important to get an interval estimate than to get a point estimate. In practical data analysis, the estimator of superiority ratio is complex as an unknown parameter, so it is difficult to obtain its accurate distribution. Therefore, it is generally necessary to search for an asymptotic confidence interval. In this paper, we use four methods to construct the asymptotic confidence interval of superiority ratio under binomial sampling. They are Delta method, Woolf method, likelihood ratio test method and saddle point approximation method. Each method has its own advantages and disadvantages. One of the innovations of this paper is to construct confidence interval of advantage ratio by saddle-point approximation method. We compare the advantages and disadvantages of these four interval estimation methods by Monte Carlo simulation. The evaluation criteria for simulation results are mainly based on the two indexes: the coverage rate of the interval to the advantage ratio true value, the degree of proximity to the confidence level and the average interval length. Finally, two empirical cases are used to demonstrate the different characteristics of the four interval estimation methods.
【作者单位】：中国人民大学应用统计科学研究中心;中国人民大学统计学院;兰州财经大学统计学院;
【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资助)项目成果(15XNL008)
【分类号】：O212.1

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