Comparison of ARIMA and GM(1,1) models for prediction of hepatitis B in China

Background Hepatitis B virus (HBV) infection is a major public health threat in China for China has a hepatitis B prevalence of more than one million people in 2017 year. Disease incidence prediction may help hepatitis B prevention and control. This study intends to build and compare 2 forecasting models for hepatitis B incidence in China. Methods Autoregressive integrated moving average (ARIMA) model and grey model GM(1,1) were adopted to fit the monthly incidence of hepatitis B in China from March 2010 to October 2017. The fitting and forecasting performances of the 2 models were evaluated. The better one was adopted to predict the incidence from November 2017 to March 2018. Database was built by Excel 2016 and statistical analysis was completed using R 3.4.3 software. Results Descriptive analysis showed that the incidence of hepatitis B in China has seasonal variation and has shown a downward trend from 2010 to 2017. We selected the ARIMA (3,1,1) (0,1,2)(12) model among all the ARIMA models for it has the lowest AIC value. Model expression of GM (1,1) was X-(1) (k + 1) = 3386876.7478e(0.0249k) - 3289206.7428. The root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) of ARIMA(3,1,1)(0,1,2)(12) model were lower than GM(1,1) model on fitting part and forecasting part. According to the forecast results, the incidence may have a slight fluctuation during the following months. Conclusions The ARIMA model showed better hepatitis B fitting and forecasting performance than GM (1,1) model. It is a potential decision supportive tool for controlling hepatitis B in China before a predictive hepatitis B outbreak.