贝叶斯层次模型在嵌套结构调查数据中的应用研究
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摘要
目的针对分层抽样流行病调查数据的结构特点,构建两种基于分层嵌套思想的贝叶斯层次模型,并探讨其优缺点。方法以贝叶斯层次模型为基础,利用嵌套结构中的层级关系构建模型,其中,模型一以嵌套层效应分解为特点构建,模型二以嵌套层效应逐级传递为特点构建。以重庆市出生缺陷调查数据为例,采用Open BUGS软件进行模型拟合及分析。结果以偏差信息准则(deviance information criterion,DIC)作为拟合优度评价,模型一和模型二的DIC值分别为101.8和101.6,大致相等;敏感性分析显示,在总体率的超参数μ设置不同先验信息下,模型一和模型二对总效应估计的变异性分别为(用标准差度量,10-4):后验均数1.191和27.546;后验中位数1.038和7.617,模型一的变异性比模型二小。结论模型一和模型二均可用于嵌套结构的调查数据建模分析及预测,拟合效果相当;但模型一比模型二受先验信息影响小,稳健性更好,更适合先验信息欠缺时的数据分析。
Objective To develop two hierarchical Bayesian models for the epidemiological data with focusing on its nested structure; as well as to explore the pros and cons of them. Methods Relationships among nested layers of nested structural data are taken into account when developing the two hierarchical Bayesian models. The first model focuses on the stratification effect of each nested layer for differentiation between the layers. The second model focuses on the transmission effect between the father layer and its son layers. Open BUGS software and a birth defects survey data were used to fit and evaluate the two hierarchical Bayesian models; and the deviance information criterion( DIC) was used for measuring the goodness-of-fit of them. A sensitivity analysis was conducted with different sets of prior information on hyper parameter of the population rate μ. Results The DIC of the two models are 101. 8 and 101. 6,respectively,which shows almost the same goodness-of-fit of them. The sensitivity analysis shows that the standard deviation of the two models for the posterior mean of estimated population rate are( 10- 4)1. 191 and 27. 546,respectively,for the posterior median of them are( 10- 4) 1. 038 and 7. 617,respectively. Both results of posterior mean and posterior median say that the first model has smaller standard deviation under different prior information scenario.Conclusion Both models can be used to model nested structural epidemiological data. However,the first model is affected by prior information much less than the second model does. Thus,the first model is more stable and is better to model nested structural survey data when little prior information is available.
Objective To develop two hierarchical Bayesian models for the epidemiological data with focusing on its nested structure; as well as to explore the pros and cons of them. Methods Relationships among nested layers of nested structural data are taken into account when developing the two hierarchical Bayesian models. The first model focuses on the stratification effect of each nested layer for differentiation between the layers. The second model focuses on the transmission effect between the father layer and its son layers. Open BUGS software and a birth defects survey data were used to fit and evaluate the two hierarchical Bayesian models; and the deviance information criterion( DIC) was used for measuring the goodness-of-fit of them. A sensitivity analysis was conducted with different sets of prior information on hyper parameter of the population rate μ. Results The DIC of the two models are 101. 8 and 101. 6,respectively,which shows almost the same goodness-of-fit of them. The sensitivity analysis shows that the standard deviation of the two models for the posterior mean of estimated population rate are( 10- 4)1. 191 and 27. 546,respectively,for the posterior median of them are( 10- 4) 1. 038 and 7. 617,respectively. Both results of posterior mean and posterior median say that the first model has smaller standard deviation under different prior information scenario.Conclusion Both models can be used to model nested structural epidemiological data. However,the first model is affected by prior information much less than the second model does. Thus,the first model is more stable and is better to model nested structural survey data when little prior information is available.
引文
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11 .王继林,樊欣.重庆市1996-2001年出生缺陷监测结果分析.中国儿童保健杂志,2003,11(3):207-209.
12 .张高东,周文正,周晓军,等.重庆市2004-2010年出生缺陷发生情况分析.华中科技大学学报,2012,41(6):759-762.
13 .Su Z,Peterman RM,Haeseker SL.Spatial hierarchical Bayesian models for stock-recruitment analysis of pink salmon(Oncorhynchusgorbuscha).Canadian Journal of Fisheries and Aquatic Sciences,2004,61(12):2471-2486.
14 .Kazembe LN,Namangale JJ.A Bayesian multinomial model to analyse spatial patterns of childhood co-morbidity in Malawi.European journal of Epidemiology,2007,22(8):545-556.
15 .Su Z,Adkison MD,Van Alen BW.A hierarchical Bayesian model for estimating historical salmon escapement and escapement timing.Canadian Journal of Fisheries and Aquatic Sciences,2001,58(8):1648-1662.
16 .Kelsall JE,Diggle PJ.Spatial variation in risk of disease:a nonparametric binary regression approach.Journal of the Royal Statistical Society(Series C),1998,47(4):559-573.
17 .Ntzoufras I.Bayesian modeling using Win BUGS.Wiley.com,2011.
18 .张俊辉,冯子健,杨超,等.基于层次贝叶斯时空模型的空间多尺度联合分析模型的构建及应用研究.中国卫生统计,2013,30(2):199-202.
2 .张尧庭,陈汉峰.贝叶斯统计推断.科学出版社,1991.
3 .Tu XM,Kowalski J,Jia G.Bayesian analysis of prevalence with covariates using simulation based techniques:applications to HIV screening.Statistics in Medicine,1999,18(22):3059-3073.
4 .王哲.多层贝叶斯方法在消费者行为中的应用研究.南京:南京航空航天大学,2012.
5 .Lindley DV,Smith AFM.Bayes estimates for the linear model.Journal of the Royal Statistical Society(Series B),1972,34(1):1-41.
6 .王建华.流行病学.北京:人民卫生出版社,2008.
7 .Daniels MJ.A prior for the variance in hierarchical models.Canadian Journal of Statistics,1999,27(3):567-578.
8 .王显红.日本血吸虫病贝叶斯时空模型的建立.北京:中国疾病预防控制中心,2007.
9 .毛萌,朱军.出生缺陷检测研究现状.实验儿科临床杂志,2009,24(11):801-803.
10 .李常惠,田宏,陈艳玲,等.辽宁省2011年度出生缺陷监测数据.中国卫生统计,2012,29(3):410-411.
11 .王继林,樊欣.重庆市1996-2001年出生缺陷监测结果分析.中国儿童保健杂志,2003,11(3):207-209.
12 .张高东,周文正,周晓军,等.重庆市2004-2010年出生缺陷发生情况分析.华中科技大学学报,2012,41(6):759-762.
13 .Su Z,Peterman RM,Haeseker SL.Spatial hierarchical Bayesian models for stock-recruitment analysis of pink salmon(Oncorhynchusgorbuscha).Canadian Journal of Fisheries and Aquatic Sciences,2004,61(12):2471-2486.
14 .Kazembe LN,Namangale JJ.A Bayesian multinomial model to analyse spatial patterns of childhood co-morbidity in Malawi.European journal of Epidemiology,2007,22(8):545-556.
15 .Su Z,Adkison MD,Van Alen BW.A hierarchical Bayesian model for estimating historical salmon escapement and escapement timing.Canadian Journal of Fisheries and Aquatic Sciences,2001,58(8):1648-1662.
16 .Kelsall JE,Diggle PJ.Spatial variation in risk of disease:a nonparametric binary regression approach.Journal of the Royal Statistical Society(Series C),1998,47(4):559-573.
17 .Ntzoufras I.Bayesian modeling using Win BUGS.Wiley.com,2011.
18 .张俊辉,冯子健,杨超,等.基于层次贝叶斯时空模型的空间多尺度联合分析模型的构建及应用研究.中国卫生统计,2013,30(2):199-202.