Bayesian Dynamic Generalized Additive Model for Mortality during COVID-19 Pandemic

While COVID-19 has resulted in a significant increase in global mortality rates, the impact of the pandemic on mortality from other causes remains uncertain. To gain insight into the broader effects of COVID-19 on various causes of death, we analyze an Italian dataset that includes monthly mortality counts for different causes from January 2015 to December 2020. Our approach involves a generalized additive model enhanced with correlated random effects. The generalized additive model component effectively captures non-linear relationships between various covariates and mortality rates, while the random effects are multivariate time series observations recorded in various locations, and they embody information on the dependence structure present among geographical locations and different causes of mortality. Adopting a Bayesian framework, we impose suitable priors on the model parameters. For efficient posterior computation, we employ variational inference, specifically for fixed effect coefficients and random effects, Gaussian variational approximation is assumed, which streamlines the analysis process. The optimisation is performed using a coordinate ascent variational inference algorithm and several computational strategies are implemented along the way to address the issues arising from the high dimensional nature of the data, providing accelerated and stabilised parameter estimation and statistical inference.