Abstract:

Objective An autoregressive integrated moving average (ARIMA) model was used to predict the monthly pulmonary tuberculosis cases in China(excluding Hong Kong, Macao and Taiwan regions) to provide a reference for pulmonary tuberculosis prevention and control. Methods Monthly pulmonary tuberculosis cases number in China from January 2006 to December 2018 reported on Disease Surveillance sponsored by CDC were collected. Based on these data, time series, preliminary identification and ordering of ARIMA model types were conducted using SPSS 26.0. Several ARIMA models were selected according to that both the simplicity of the model and the parameters of the ARIMA model (including autoregressive method (AR), average moving method (MA), seasonal autoregressive method (SAR), seasonal moving average method (SMA)) were statistically significant (Ps<0.05), as well as the overall test index (Ljung-Box Q value), maximum stationary coefficient (R ²) of the model, standardized Bayesian information criterion value (NBIC) of the smallest overall model, and minimum root mean square error (RMSE). Numbers of reported cases from January to August 2019 were used as verification, and the model with the smallest relative error was selected as the optimal model according to that the smaller the relative error of the predicted value, the better the model; finally, the model was used to predict monthly reported numbers of tuberculosis patients from September 2019 to December 2020 in China. Results Time series were based on cases from January 2006 to December 2018, the fitted model was ARIMA (p, d, q) or ARIMA (p, d, q)×(P, D, Q). Twelve models were selected according to P value (which is relative to Ljung-Box Q)>0.05,the simplicity of the model, and parameters of the model were statistically significant (all P<0.05); and models with the maximum R ² (ARIMA (1, 0, 1) (0, 1, 1)₁₂, R ²=0.707)), or with the minimum RMSE (ARIMA (0, 1, 2) (0, 1, 1)₁₂, RMSE=9147.85), or with the minimum NBIC (ARIMA (0, 1, 1) (0, 1, 1)₁₂, NBIC=18.355)), or with the minimum Ljung-Box Q (ARIMA (1, 1, 1) (0, 1,1)₁₂, Ljung-Box Q=8.797)) were taken as alternatve models, to predict numbers of reported cases from January to August 2019, which were then compared with the actual data, to determine the optimal ARIMA model (ARIMA (0, 1, 1) (0, 1, 1)₁₂ model), with the relative error was the smallest (0.55%), MA (1)=0.875 (t=19.243, P<0.001), SMA (1)=0.876 (t=7.596, P<0.001), Ljung-Box Q=9.876 (df=16, P=0.873). The ARIMA (0, 1, 1) (0, 1, 1)₁₂ model was used to predict numbers of monthly reported tuberculosis cases in China from September 2019 to December 2020; in 2020 year, there will be 1025863 cases totally with average of 85489 cases monthly. Conclusion ARIMA (0, 1, 1) (0, 1, 1)₁₂ model is the better model to predict the monthly pulmonary tuberculosis cases in China. However, in order to improve accuracy of the prediction, the establishment and prediction of the model is a dynamic process needed to be adjusted continuously according to accumulated data.

Key words: Tuberculosis, pulmonary, Disease notification, Epidemiologic research design, Models, statistical, Forecasting