GM(1,1)灰色模型、马尔可夫链模型及其组合模型和SARIMA模型在甲肝发病数预测中的应用效果比较  

Comparisons of GM(1,1) gray model,Markov chain model,their combined model,and SARIMA model in predicting monthly reported caseload of hepatitis A

作　　者：刘天[1] 王芸[2] 姚梦雷[1] 黄继贵[1] 吴杨[3] 童叶青[3] LIU Tian;WANG Yun;YAO Meng-lei;HUANG Ji-gu;WU Yang;TONG Ye-qing(Jingzhou Municipal Center for Disease Control and Prevention,Jingzhou 434000,China;Qingyang City Center for Disease Control and Prevention;Hubei Provincial Center for Disease Control and Prevention)

机构地区：[1]荆州市疾病预防控制中心,湖北荆州434000 [2]庆阳市疾病预防控制中心 [3]湖北省疾病预防控制中心

出　　处：《华南预防医学》2019年第2期128-132,共5页South China Journal of Preventive Medicine

基　　金：湖北省卫生计生委创新团队项目(WJ2016JT-002)

摘　　要：目的比较GM(1,1)灰色模型、马尔可夫链模型及其组合模型和SARIMA模型在甲肝发病数预测中的应用效果。方法利用2010—2014年江西省甲肝逐月发病数数据,分别拟合GM(1,1)灰色模型、马尔可夫链模型、灰色马尔可夫链组合模型和SARIMA模型。利用4个模型预测2015年1—12月甲肝发病数并与实际值比较,采用平均绝对百分比误差(MAPE)、平均误差率(MER)、均方误差(MSE)和平均绝对误差(MAE)4个指标评模型预测效果。结果 2010—2015年江西省累计报告甲肝2 939例,甲肝发病数整体呈逐年下降趋势(r_s=-0.838,P<0.01)。SARIMA(0,1,1)(1,0,0)12为最优SARIMA模型;GM(1,1)灰色模型拟合精度为合格。模型预测的MAPE从低到高依次为灰色马尔可夫链组合模型(23.894%)、SARIMA模型(25.529%)、GM(1,1)灰色模型(28.429%)、马尔可夫链模型(39.426%);MER从低到高依次为SARIMA模型(21.303%)、灰色马尔可夫链组合模型(25.574%)、灰色模型(30.717%)、马尔可夫链模型(35.203%);MSE和MAE从低到高依次均为SARIMA模型(45.293、4.918)、灰色马尔可夫链组合模型(47.122、5.903)、灰色模型(67.738、7.091)、马尔可夫链模型(85.252、8.126)。结论灰色马尔可夫链组合模型和SARIMA模型预测效果较好,可以用于甲肝发病数的预测。Objective To compare effects of GM(1,1)gray model,Markov chain model,the gray and Markov chain combined model,and SARIMA model on predicting monthly reported cases of hepatitis A. Methods Using data of monthly reported cases of hepatitis A in Jiangxi Province from 2010 to 2014,GM(1,1)gray model,Markov chain model,combined model of gray and Markov chain,and SARIMA model were fitted respectively. Four models were used to predict the monthly reported cases of hepatitis A from January to December 2015 and compare with actual number of cases. The mean absolute percent error(MAPE),mean error rate(MER),mean squared error(MSE)and mean absolute error(MAE)were used to evaluate the model prediction effect. Results A total of 2 939 cases of hepatitis A were reported in Jiangxi Province during this period,and showed a downtrend year by year(rs=-0.838,P<0.01).SARIMA(0,1,1)(1,0,0)12 was the optimal SARIMA model;the fitting accuracy of GM(1,1)gray model was qualified. The model predicted MAPE from low to high were the gray Markov chain combined model(23.894%),SARIMA model(25.529%),GM(1,1)gray model(28.429%),and Markov chain model(39.426%)).MER from low to high were SARIMA model(21.303%),gray Markov chain combined model(25.574%),gray model(30.717%),and Markov chain model(35.203%).MSE and MAE from low to high were the SARIMA model(45.293,4.918),gray Markov chain combined model(47.122,5.903),gray model(67.738,7.091),and Markov chain model(85.252,8.126). Conclusions The grey Markov chain combined model and SARIMA model have better prediction results,and can be used to predict the number of hepatitis A cases.

关 键 词：模型 统计学 肝炎 甲型 预测 

分 类 号：R183.7[医药卫生—流行病学]