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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (2): 136-142    DOI:
    
Confidence interval construction for the incidence of chronic diseases
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  In epidemiological studies, incidence of a disease is an important index which reflects the degree of the onset of a certain disease in the particular crowd. As a result, the structure of the confidence interval of it has important medical significance in judging disease extent. For some chronic diseases (such as cancer or cardiovascular, etc.), due to their long onset period and low incidence, Poisson sampling is in accord with the facts more than binomial sampling and inverse sampling. Four methods were used to study the construction of confidence interval for the incidence of chronic diseases under poisson distribution, and the performance properties of the four methods were compared through monte carlo simulation. Simulation results show that when higher incidence, pivot method did very well in both coverage and the interval length. When rates are relatively lower, pivot method is slightly inferior to Wald statistic method and the method of scoring on the interval length, but it did the best on the coverage. As a result, the overall performance of pivot method is very good.

Key words： incidence of a diseases      Poisson sampling      the estimation of confidence intervals      Monte Carlo simulation     
Received: 03 September 2015      Published: 17 May 2018
CLC:  O212.4  
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BAI Yong-xin, TIAN Mao-zai. Confidence interval construction for the incidence of chronic diseases. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 136-142.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I2/136


慢性病发病率置信区间的构造

在流行病研究中, 发病率是一个重要指标, 该指标反映的是特定人群中某种疾病的发病程度. 因此, 对它的置信区间的构造在判别疾病发病程度上具有重要的医学意义. 对于一些慢性疾(如癌症或心血管等), 由于其发病周期长, 发病率低, Poisson抽样下要比二项抽样, 逆项抽样更符合事实. 利用四种方法研究了泊松分布下慢性病发病率的置信区间构造, 并通过Monte Carlo模拟对四种方法的表现性能进行比较. 模拟结果表明: 当发病率较高时, 枢轴量方法无论在区间长度还是覆盖率上都表现最佳；当发病率相对较低时, 枢轴量方法在区间长度上略次于Wald统计量方法和得分方法,但是在覆盖率上表现最佳. 因此, 枢轴量方法整体上表现的很好.

关键词： 发病率,  Poisson抽样,  区间估计,  Monte Carlo模拟 
[1] BAI Yong-xin, TIAN Mao-zai. Confidence interval construction for the risk difference of chronic disease based on saddle-point approximation under poisson distribution[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 253-266.