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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (3): 253-266    DOI:
    
Confidence interval construction for the risk difference of chronic disease based on saddle-point approximation under poisson distribution
BAI Yong-xin1, TIAN Mao-zai1,2
1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China
2. Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China
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Abstract  Risk is one of the important indicators in the epidemiology and usually used to compare the effectiveness of two therapeutics or diagnostics. Therefore, accurate estimate of the risk difference interval is important for the diagnosis of disease and selection of therapeutic scheme. Combining with the characteristics of chronic whose diseases cycle is long and the incidence is low and the advantages of Poisson sampling, the paper uses the saddle point approximation method to construct the risk difference confidence interval under the Poisson distribution. At the same time, five traditional kinds of interval estimation method are assessed through examples and monte carlo simulation. Simulation results show that under the condition of small samples, the saddle point approximation is a kind of very good confidence interval estimation method. In most cases it can guarantee the coverage rate being equal to the desired confidence level and make the shortest length.

Key words： Poisson distribution      saddle point approximation      Monte Carlo simulation      confidence interval      
Received: 11 August 2016      Published: 07 April 2018
CLC:  O212  
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BAI Yong-xin, TIAN Mao-zai. Confidence interval construction for the risk difference of chronic disease based on saddle-point approximation under poisson distribution. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 253-266.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I3/253


Poisson分布下基于鞍点逼近的慢性病风险差的置信区间构造

风险差是流行病学中重要的指标之一，常用来比较两种治疗或两种诊断的有效性. 因此, 风险差区间的精确估计对流行病病情的诊断以及治疗方案的选择有很重要的意义. 结合Poisson抽样的优点以及慢性病发病周期长和发病率低的特点， 利用鞍点逼近方法来构造了Poisson分布下风险差的置信区间. 同时, 通过实例和Monte Carlo模拟对传统的四种区间构造方法进行评价. 模拟结果表明: 在小样本情况下, 鞍点逼近方法得到的置信区间大多数能保证覆盖率近似于期望的置信水平并且使得区间长度最短, 是一种很好的置信区间构造方法.

关键词： Poisson分布,  鞍点逼近,  Monte Carlo模拟,  置信区间 
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