A single autoregressive integrated moving average with exogenous variable outperforms ensembles of autoregressive models for forecasting influenza hospitalizations in the contiguous United States

Infectious disease forecasting is important to public health decision-making, particularly for mitigating the burden of seasonal influenza. We propose and evaluate comprehensive autoregressive modelling approaches (autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average with exogenous variables (ARIMAX)) for short-term forecasts of influenza-related hospitalizations across the contiguous United States (US). We used data from the National Healthcare Safety Network to forecast the influenza seasons of the years 2022 to 2024 in 48 states. We compare automatically tuned models (AUTO) and ensembles of different sizes (ES27 or ES64). Base models are ARIMA models or ARIMAX models using forecasting covariates with a one-week lag of the forecast day, including: mean temperature, mean hospitalizations by epidemiological weeks, mean hospitalizations in adjacent states and the average of hospitalizations across the contiguous US. We also investigated the effect of forecasting based on log-transformed hospitalizations data and back-transforming the results (LB). Overall, 29 approaches were compared to the AUTO ARIMA model without logarithmic transformation and the FluSight baseline using weighted interval scores. Our results indicate that using the LB approach, which forecasts based on epidemic growth rate and back-transform the results, most increased model performance. The average of hospitalizations across the contiguous US (AVG) forecasting feature was the most useful covariate. Ensemble approaches typically did not improve performance. The best model was the AUTO ARIMAX using the AVG covariate with log-back transformation.