Expanding optimization ensemble model methods for forecasting seasonal influenza in the U.S

Each year, the seasonal influenza epidemic sees significant variability in its evolution. Accurate forecasts of future influenza cases are important for planning public health responses. The United States Centers for Disease Control and Prevention (CDC) has annually organized the FluSight competition (https://github.com/cdcepi/FluSight-forecast-hub) to solicit forecasts from participating teams over horizons of 0, 1, 2, and 3 weeks ahead. Using these data, the CDC produces an ensemble forecast of all submitted forecasts. In this paper, we introduce a new weight-based ensemble forecasting method to consider predicting laboratory-confirmed influenza hospital admissions for the 2024-2025 season. The method consists of determining optimal weights that are updated week-by-week throughout the FluSight competition to minimize the mean squared error (MSE) of a blend of teams' previous forecasts compared to the truth data. Using these weights over an expanding time window starting at the beginning of the season (late Fall), we produce our own future forecasts; we call our method the expanding window optimization (EWO). The results indicate that EWO achieves superior average performance compared to the CDC ensemble, exhibiting lower mean absolute error (MAE) and weighted interval score (WIS) across all forecast horizons. To further improve performance, the adjusted weighted-EWO (Adw-EWO) is introduced, which augments EWO with a correction term governed by a parameter π ∈ (0, 1) derived from horizon-0 forecast errors and applied uniformly across horizons. Adw-EWO yields additional improvements, particularly at horizon 0. Phase-based analysis reveals that Adw-EWO performs optimally during epidemic growth and peak periods, whereas EWO is effective in early growth but less robust under abrupt changes. In contrast, the CDC ensemble performs better during the decay phase.