Forecasting Influenza Hospitalizations Using a Bayesian Hierarchical Nonlinear Model with Discrepancy

The annual influenza outbreak leads to significant public health and economic burdens making it desirable to have prompt and accurate probabilistic forecasts of the disease spread. The United States Centers for Disease Control and Prevention (CDC) hosts annually a national flu forecasting competition which has led to the development of a variety of flu forecast modeling methods. Beginning in 2013, the target to be forecast was weekly percentage of patients with an influenza-like illness (ILI), but in 2021 the target was changed to weekly hospitalizations. Reliable hospitalization data has only been available since 2021, but ILI data has been available since 2010 and has been successfully forecast for several seasons. In this manuscript, we introduce a two component modeling framework for forecasting hospitalizations utilizing both hospitalization and ILI data. The first component is for modeling ILI data using a nonlinear Bayesian model. The second component is for modeling hospitalizations as a function of ILI. For hospitalization forecasts, ILI is first forecast then hospitalizations are forecast with ILI forecasts used as a predictor. In a simulation study, the hospitalization forecast model is assessed and two previously successful ILI forecast models are compared. Also assessed is the usefulness of including a systematic model discrepancy term in the ILI model. Forecasts of state and national hospitalizations for the 2023-24 flu season are made, and different modeling decisions are compared. We found that including a discrepancy component in the ILI model tends to improve forecasts during certain weeks of the year. We also found that other modeling decisions such as the exact nonlinear function to be used in the ILI model or the error distribution for hospitalization models may or may not be better than other decisions, depending on the season, location, or week of the forecast.