ARIMA模型在全国丙型肝炎疫情预测中的应用

Applications of autoregressive integrated moving average model on prediction of incidence of hepatitis C

目的 探讨应用时间序列基于季节性差分的自回归移动平均模型（autoregressive integrated moving average,ARIMA）预测全国丙型肝炎的发病情况。方法 利用“中国疾病预防控制信息系统”中的“疾病监测信息报告管理系统”（又称“传染病疫情信息网络直报系统”）的资料,应用SPSS 19.0统计软件、采用ARIMA模型,对全国2005年1月~2012年12月丙型肝炎逐月发病数进行建模和拟合,利用所得到的模型对2013年1~6月的发病情况进行预测,并按照预测值与实际观察值之间的差异评价其预测效果。结果 分析结果显示,丙型肝炎发病以年为周期,一年中3~5月为高发月。非季节自回归参数为5.84,t=-2.567,P=0.012。非季节移动平均参数为0.481,t=3.392,P=0.001,季节移动平均参数为0.625,t=3.547,P=0.001,差异有统计学意义。BIC=14.162,Ljung-Box统计量检验残差序列为白噪声序列,预测的平均相对误差为3.4%,丙型肝炎拟合的最佳模型为ARIMA（1,1,1）,（0,1,1）12。结论ARIMA对全国丙型肝炎拟合的预测效果较为满意,预测结果将为今后丙型肝炎等多种传染病的预防和控制提供理论支持。

Objective To evaluate the value of application of autoregressive integrated moving average （ARIMA） on prediction of the incidence of hepatitis C. Methods Data were collected from the ＂China Disease Prevention and Control Information System＂. The ARIMA model was established based on the monthly incidence numbers of hepatitis C in China from January 2005 to June 2013 by SPSS 19.0 software, and the differences between predicted values and the actual values were evaluated. Results The incidence of hepatitis C presented an annual cycle, with high-risk month of march to May. The seasonal autoregressive parameter was 5.84 （t=2.567, P=0. 012）. The season moving average parameter was 0.481 （t=3.392, P= 0. 001）. The season moving average parameter was 0. 625 （t=3. 547, P= 0. 001）. BIC was 14. 162. Ljung-Box statistic test residue was white noise sequence. The average relative error of prediction was 3.4%. The best fitting model of hepatitis C was ARIMA （1, 1, 1）, （0, 1, 1）12. Conclusions The ARIMA model is suitable for forecasting incidence of hepatitis C in China. It can also be used in prediction of incidence of other infectious diseases.