对角膨胀双变量Poisson回归模型在结核病影响因素分析中的应用
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摘要
结核病的传播过程比较复杂,易感人群在受到结核病菌传染后可能会患上结核病或结核性胸膜炎,前者具有传染性,而后者暂时不具有传染性,但可能又会发展成结核病,具有传染性.为了探讨结核病的影响因素,利用对角膨胀双变量Poisson回归模型,将受结核病菌传染所发生的结核病患者数和结核性胸膜炎患者数作为模型中的2维响应变量,拟合D市在校学生受结核病菌传染的患病数据.计算结果表明:结核病患者与结核性胸膜炎患者不具有相关性;强阳率、痰菌检验阳性状态、宿舍密度、季节与通风状态差等因素是对结核病的影响因素,数据拟合效果较好,为对结核病的预防工作提供参考依据.
The spread of tuberculosis is complicated, and susceptible people may develop tuberculosis or tuberculous pleurisy after being infected with tubercle bacillus. Tuberculosis is contagious, while tuberculous pleurisy is not contagious for the time being, but it may develop into tuberculosis. The diagonal inflated bivariate Poisson regression model is useful to exploring the influencing factors of tuberculosis infection. We consider the number of tuberculosis patients and tuberculous pleurisy patients infected with tubercle bacillus as the 2-dimensional response variables in the model, to fit the data of students infected with tubercle bacillus in D city. The calculation results show that there is no correlation between tuberculosis patients and tuberculous pleurisy patients, and strong positive rate, positive test of sputum bacteria,density of dormitory, season and poor ventilation and other factors can affect tuberculosis.The data fitting effect is better, which provides a reference for the prevention of tuberculosis.
The spread of tuberculosis is complicated, and susceptible people may develop tuberculosis or tuberculous pleurisy after being infected with tubercle bacillus. Tuberculosis is contagious, while tuberculous pleurisy is not contagious for the time being, but it may develop into tuberculosis. The diagonal inflated bivariate Poisson regression model is useful to exploring the influencing factors of tuberculosis infection. We consider the number of tuberculosis patients and tuberculous pleurisy patients infected with tubercle bacillus as the 2-dimensional response variables in the model, to fit the data of students infected with tubercle bacillus in D city. The calculation results show that there is no correlation between tuberculosis patients and tuberculous pleurisy patients, and strong positive rate, positive test of sputum bacteria,density of dormitory, season and poor ventilation and other factors can affect tuberculosis.The data fitting effect is better, which provides a reference for the prevention of tuberculosis.
引文
[1] Hogate P. Estimation for the bivariate Poisson distribution[J]. Biometrika, 1964, 51(2):241-245.
[2] Kocherlakota S,Kocherlakota J. Bivariate Discrete Distributions[M]. New York:Marcel Dekker,1992:81-121.
[3] Kocherlakota, S,Kocherlakota, K. Regression in the bivariate Poisson distribution[J]. Communications in Statistics-Theory and Methods, 2001, 30(5), 815-827.
[4] Walhin, J. F.(2001), Bivariate ZIP models[J]. Biometrical Journal 43, 147-160.
[5] Karlis D, Ntzoufras I. Analysis of sports data by using bivariate Poisson models[J]. Journal of the Royal Statistical Society, 2003, 52(3):381-393.
[6]侯文,王冰,孟彦彤,等.基于对角膨胀双变量Poisson模型的中超联赛赛事数据分析[J].数学的实践与认识,2018, 48(01):168-175.
[7]梁晓琳,李二倩,田茂再·多元广义泊松分布的参数估计与诊断[J].系统科学与数学,2017, 37(5):1319-1334
[8]解锋昌,韦博成,林金官.零过多数据的统计分析及其应用[M].北京:科学出版社,2013:1-8.
[9] Dempster A, Laird N, Rubin D. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society B, 1977, 39(1):1-38.
[10] Efron B. Bootstrap Methods:Another Look at the Jackknife[J]. Annals of Statistics, 1992, 7(1):1-26.
[11]何广学,王林,杜昕等.结核病感染危险和传染参数的估算与分析[J].中国公共卫生,2003, 19(7):867-868.
[12]童叶青,郭慧,叶建军等.武汉市社区人群结核病防治核心知识知晓情况及影响因素分析[J].中国卫生统计,2016, 33(1):107-109.
[13] Lin T H, Tsai M H. Modeling health survey data with excessive zero and K responses[J]. Statistics in Medicine, 2013, 32(9):1572-1583.
[2] Kocherlakota S,Kocherlakota J. Bivariate Discrete Distributions[M]. New York:Marcel Dekker,1992:81-121.
[3] Kocherlakota, S,Kocherlakota, K. Regression in the bivariate Poisson distribution[J]. Communications in Statistics-Theory and Methods, 2001, 30(5), 815-827.
[4] Walhin, J. F.(2001), Bivariate ZIP models[J]. Biometrical Journal 43, 147-160.
[5] Karlis D, Ntzoufras I. Analysis of sports data by using bivariate Poisson models[J]. Journal of the Royal Statistical Society, 2003, 52(3):381-393.
[6]侯文,王冰,孟彦彤,等.基于对角膨胀双变量Poisson模型的中超联赛赛事数据分析[J].数学的实践与认识,2018, 48(01):168-175.
[7]梁晓琳,李二倩,田茂再·多元广义泊松分布的参数估计与诊断[J].系统科学与数学,2017, 37(5):1319-1334
[8]解锋昌,韦博成,林金官.零过多数据的统计分析及其应用[M].北京:科学出版社,2013:1-8.
[9] Dempster A, Laird N, Rubin D. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society B, 1977, 39(1):1-38.
[10] Efron B. Bootstrap Methods:Another Look at the Jackknife[J]. Annals of Statistics, 1992, 7(1):1-26.
[11]何广学,王林,杜昕等.结核病感染危险和传染参数的估算与分析[J].中国公共卫生,2003, 19(7):867-868.
[12]童叶青,郭慧,叶建军等.武汉市社区人群结核病防治核心知识知晓情况及影响因素分析[J].中国卫生统计,2016, 33(1):107-109.
[13] Lin T H, Tsai M H. Modeling health survey data with excessive zero and K responses[J]. Statistics in Medicine, 2013, 32(9):1572-1583.