A spatio-temporal model with seasonality to analyze elderly mortality patterns in Italy

Bayesian spatio-temporal models are particularly effective in disease mapping, enabling the smoothing of relative risks and the monitoring of their temporal and spatial variations. Motivated by the study of mortality risk in the elderly population across Italian provinces, we propose an extended model that also accounts for seasonal variations. These seasonal patterns prove highly informative for understanding the impact of major events, such as the COVID-19 pandemic and heatwaves. The inclusion of seasonality increases both the number of interaction effects and the overall complexity of the model. Additionally, specifying meaningful prior distributions for the variance parameters of random effects is challenging due to the influence of model design and correlation structures. To ensure balanced prior variability among model components, we adopt the Design and Structure Dependent (DSD) prior specification approach, which appears to be an intuitive prior elicitation strategy, even for practitioners. Analysis of the results from the proposed model provides valuable insights into the phenomenon under study, including a quantification of the impacts of the first and second waves of COVID-19 and the differing effects of unusually warm summer seasons across regions.