Forecasting influenza hospital admissions within English sub-regions using hierarchical generalised additive models

Seasonal influenza places a substantial burden annually on healthcare services. Policies during the COVID-19 pandemic limited the transmission of seasonal influenza, making the timing and magnitude of a potential resurgence difficult to ascertain and its impact important to forecast.

We have developed a hierarchical generalised additive model (GAM) for the short-term forecasting of hospital admissions with a positive test for the influenza virus sub-regionally across England. The model incorporates a multi-level structure of spatio-temporal splines, weekly cycles in admissions, and spatial correlation. Using multiple performance metrics including interval score, coverage, bias, and median absolute error, the predictive performance is evaluated for the 2022-2023 seasonal wave. Performance is measured against autoregressive integrated moving average (ARIMA) and Prophet time series models.

Across the epidemic phases the hierarchical GAM shows improved performance, at all geographic scales relative to the ARIMA and Prophet models. Temporally, the hierarchical GAM has overall an improved performance at 7 and 14 day time horizons. The performance of the GAM is most sensitive to the flexibility of the smoothing function that measures the national epidemic trend.

This study introduces an approach to short-term forecasting of hospital admissions for the influenza virus using hierarchical, spatial, and temporal components. The methodology was designed for the real time forecasting of epidemics. This modelling framework was used across the 2022-2023 winter for healthcare operational planning by the UK Health Security Agency and the National Health Service in England.