Applying SARIMA, ETS, and hybrid models for prediction of tuberculosis incidence rate in Taiwan

Tuberculosis (TB) remained one of the world's most deadly chronic communicable diseases. Future TB incidence prediction is a benefit for intervention options and resource-allocation planning. We aimed to develop rapid univariate prediction models for epidemics forecasting employment.

The surveillance data regarding Taiwan monthly TB incidence rates which from January 2005 to June 2017 were utilized for simulation modelling and from July 2017 to December 2020 for model validation. The modeling approaches including the Seasonal Autoregressive Integrated Moving Average (SARIMA), the Exponential Smoothing (ETS), and SARIMA-ETS hybrid algorithms were constructed and compared. The modeling performance of in-sample simulating training sets and pseudo-out-of-sample validating sets were evaluated by metrics of the root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), and mean absolute scaled error (MASE).

A total of 191,526 TB cases with a highest incidence rate in 2005 (72.5 per 100,000 person-year) and lowest in 2020 (33.2 per 100,000 person-year), from January-2005 to December-2020 showed a seasonality and steadily declining trend in Taiwan. The monthly incidence rates data were utilized to formulate these forecasting models. Through stepwise screening and assessing of the accuracy metrics, the optimized SARIMA(3,0,0)(2,1,0)₁₂, ETS(A,A,A) and SARIMA-ETS-hybrid models were respectively selected as the candidate models. Regarding the outcome assessment of model performance, the SARIMA-ETS-hybrid model outperformed the ARIMA and ETS in the short term prediction with metrics of RMSE, MAE MAPE, and MASE of 0.084%, 0.067%, 0.646%, and 0.870%, during the pseudo-out-of-sample forecasting period. After projecting ahead to the long term forecasting TB incidence rates, ETS model showed the best performance resulting as a 41.69% (range: 22.1-56.38%) reduction of TB epidemics in 2025 and a 54.48% (range: 33.7-68.7%) reduction in 2030 compared with the 2015 levels.

This time series modeling might offer us a rapid surveillance tool for facilitating WHO's future TB elimination milestone. Our proposed SARIMA-ETS or ETS model outperformed the SARIMA in predicting less or 12-30 months ahead of epidemics, and all models showed better in short or medium-term forecasting than long-term forecasting.