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Weighted ensemble learning outperforms statistical, machine-learning, and deep-learning models for varicella
Yan Liu1, Tao Ma2, Yingying Shi3
1Liuhe District Center for Disease Control and Prevention, Nanjing, China.
Background:
Varicella imposes a sustained public health burden in China, where decades of voluntary single-dose immunization have been associated with recurrent school outbreaks and an age shift toward adolescents. Accurate forecasting of varicella incidence is crucial for public health preparedness and resource allocation. Systematic head-to-head benchmarks of statistical, machine-learning, deep-learning, and ensemble forecasts for varicella in Chinese metropolitan settings are scarce.
Methods:
Monthly varicella case counts for Nanjing, China (January 2015-December 2025) were extracted from the Chinese Notifiable Infectious Disease Reporting System. Trend, seasonality, and multi-year periodicity were characterized using the Mann-Kendall test, Theil-Sen estimator, STL decomposition, Lomb-Scargle periodogram, and continuous wavelet transform. Twelve models, SARIMA, ETS, TBATS, Prophet, random forest, XGBoost, support vector regression, NNAR, LSTM, and three ensembles (simple averaging, inverse-RMSE weighting, Ridge-stacked generalization), were trained on 108 months and evaluated on a pre-specified 24-month hold-out (2024-2025) using RMSE, MAE, MAPE, sMAPE, and R2. The optimal model was retrained on the full series to generate 2026-2027 baseline projections with bootstrap 95% prediction intervals.
Results:
Incidence rose significantly (Kendall's τ = 0.34, p < 0.001; Theil-Sen slope 2.57 cases/month) with strong annual seasonality (F s = 0.82), a primary November-December peak, a secondary May-June surge, and a wavelet-detected biennial mode intensifying after 2019. The inverse-RMSE weighted ensemble outperformed all 11 competitors (RMSE 133.49; MAPE 19.30%; R 2 = 0.74), reducing RMSE by 23.7% versus XGBoost and 44.6% versus SARIMA, and surpassing Ridge-stacked meta-learning under the moderate sample size. Forecasts projected 9,980 and 10,210 cases for 2026 and 2027, respectively.
Conclusion:
A transparently weighted ensemble delivered the most accurate short-term varicella forecasts for Nanjing, aligning with international forecast-hub practice and providing a pre-registered baseline for evaluating Jiangsu's two-dose policy.