逆抽样下流行病发病率的逼近与渐近置信区间

田茂再;吴喜之;李远;周朋朋

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (5) : 513-523.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (5) : 513-523. DOI: 10.12341/jssms10102
论文

逆抽样下流行病发病率的逼近与渐近置信区间

    田茂再, 吴喜之, 李远, 周朋朋
作者信息 +

Approximate and Asymptotic Confidence Intervals for Epdemiologic Rate under Inverse Sampling

    TIAN Maozai, WU Xizhi, LI Yuan, ZHOU Pengpeng
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摘要

流行病研究的重要任务之一就是较为精确地估计出疾病的流行程度. 疾病的流行性通常用发病率来表征. 由于置信区间估计是一种体现对发病率估计好坏的途径,所以它是估计边限的重要提示物.作者在逆抽样条件下探究了7种流行病发病率的逼近与渐近的置信区间估计.通过蒙特卡罗方法, 广泛地比较了这些方法的表现性能. 为了方便今后进一步应用此结果,制做了许多相应的表格. 这些表格清楚地表明为了构造出具有指定期望值的置信区间所需要的最小病例数. 模拟的结果表明: 就流行病发病率的区间估计的覆盖率与区间大小的稳定性而言, 逼近与渐近方法要优越于精确方法. 更多的研究表明:鞍点逼近型置信区间就控制覆盖率和平均区间长度而言表现得最好,因此,在实际应用中如果能得到,建议尽量使用它.

Abstract

One of the important tasks in epidemiological investigations is to estimate the prevalence of the disease. As confidence interval estimator is one way to represent how ``good" an estimate is, it is an important reminder of the limitations of the estimates. In this paper, we'll explore seven approximate and asymptotic confidence interval estimators for epidemiologic rate under
inverse sampling. Extensive comparisons of their performance is completed
by Monte Carlo simulation. To facilitate further the application of the results given in this paper, we present lots of tables which clearly indicate the minimum required number of cases for the ratio of the expected size of a confidence interval. Simulation results show that these approximate and asymptotic methods are better than exact ones for interval estimation of the epidemic rate p in the case of the stability of coverage probability and size. Applications to real data are also presented.

关键词

逼近与渐近置信区间 / F-逼近 / χ2-逼近 / 鞍点逼近 / 逆抽样

Key words

Approximate and asymptotic confidence interval / F-approximations / χ2-approximations / saddlepoint approximations / inverse sampling

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田茂再 , 吴喜之 , 李远 , 周朋朋. 逆抽样下流行病发病率的逼近与渐近置信区间. 系统科学与数学, 2008, 28(5): 513-523. https://doi.org/10.12341/jssms10102
TIAN Maozai , WU Xizhi , LI Yuan , ZHOU Pengpeng. Approximate and Asymptotic Confidence Intervals for Epdemiologic Rate under Inverse Sampling. Journal of Systems Science and Mathematical Sciences, 2008, 28(5): 513-523 https://doi.org/10.12341/jssms10102
中图分类号： 62G05    62G20    60G42   
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