Bayesian nowcasting for delay adjustments using time-varying parametric functions of cumulative reporting probability

Timely and accurate estimates of disease cases are crucial for effective public health responses, but reporting delays often obscure the true number of cases, complicating real-time surveillance. This paper introduces a novel Bayesian hierarchical model designed to nowcast true case counts by addressing reporting delays. The model employs flexible parametric forms to track the cumulative reporting proportion over time and incorporates time-varying parameters to adjust for changes in reporting behavior. These time-varying parameters are modeled as stochastic processes, such as random walks to ensure smoothness or Ornstein-Uhlenbeck (OU) processes to introduce mean-reverting behavior. Our approach enhances the accuracy and adaptability of nowcasting in complex and realistic scenarios. We assess the performance of the model through simulation studies and real-world applications. In simulations across 6 different scenarios, including fully and non-fully reported cases, our proposed model outperforms traditional nowcasting methods. Real-world data further demonstrate that the model can produce reliable estimates of true case counts even in the presence of significant reporting delays, revealing substantial underreporting in actual cases. Our findings highlight that combining flexible parametric modeling with time-varying adjustments significantly improves nowcasting accuracy, particularly in dynamic reporting environments. This model serves as a robust and adaptable tool for real-time disease surveillance, allowing health authorities to make more informed and timely decisions based on current case data.