Early Warning and Prediction of Scarlet Fever in China Using the Baidu Search Index and Autoregressive Integrated Moving Average With Explanatory Variable (ARIMAX) Model: Time Series Analysis

BACKGROUND: Internet-derived data and the autoregressive integrated moving average (ARIMA) and ARIMA with explanatory variable (ARIMAX) models are extensively used for infectious disease surveillance. However, the effectiveness of the Baidu search index (BSI) in predicting the incidence of scarlet fever remains uncertain. OBJECTIVE: Our objective was to investigate whether a low-cost BSI monitoring system could potentially function as a valuable complement to traditional scarlet fever surveillance in China. METHODS: ARIMA and ARIMAX models were developed to predict the incidence of scarlet fever in China using data from the National Health Commission of the People’s Republic of China between January 2011 and August 2022. The procedures included establishing a keyword database, keyword selection and filtering through Spearman rank correlation and cross-correlation analyses, construction of the scarlet fever comprehensive search index (CSI), modeling with the training sets, predicting with the testing sets, and comparing the prediction performances. RESULTS: The average monthly incidence of scarlet fever was 4462.17 (SD 3011.75) cases, and annual incidence exhibited an upward trend until 2019. The keyword database contained 52 keywords, but only 6 highly relevant ones were selected for modeling. A high Spearman rank correlation was observed between the scarlet fever reported cases and the scarlet fever CSI (r(s)=0.881). We developed the ARIMA(4,0,0)(0,1,2)((12)) model, and the ARIMA(4,0,0)(0,1,2)((12)) + CSI (Lag=0) and ARIMAX(1,0,2)(2,0,0)((12)) models were combined with the BSI. The 3 models had a good fit and passed the residuals Ljung-Box test. The ARIMA(4,0,0)(0,1,2)((12)), ARIMA(4,0,0)(0,1,2)((12)) + CSI (Lag=0), and ARIMAX(1,0,2)(2,0,0)((12)) models demonstrated favorable predictive capabilities, with mean absolute errors of 1692.16 (95% CI 584.88-2799.44), 1067.89 (95% CI 402.02-1733.76), and 639.75 (95% CI 188.12-1091.38), respectively; root mean squared errors of 2036.92 (95% CI 929.64-3144.20), 1224.92 (95% CI 559.04-1890.79), and 830.80 (95% CI 379.17-1282.43), respectively; and mean absolute percentage errors of 4.33% (95% CI 0.54%-8.13%), 3.36% (95% CI –0.24% to 6.96%), and 2.16% (95% CI –0.69% to 5.00%), respectively. The ARIMAX models outperformed the ARIMA models and had better prediction performances with smaller values. CONCLUSIONS: This study demonstrated that the BSI can be used for the early warning and prediction of scarlet fever, serving as a valuable supplement to traditional surveillance systems.