A joint hierarchical model for the number of cases and deaths due to COVID-19 across the boroughs of Montreal

Abstract

Montreal has been the epicentre of the COVID-19 pandemic in Canada with the highest number of deaths in the country. The cumulative numbers of cases and deaths, as of July 25th, 2021, recorded in the 33 areas of Montreal are modelled through a bivariate hierarchical Bayesian model using Poisson distributions. The Poisson means are decomposed in the log scale as the sums of fixed effects and latent effects. The areal median age, the educational level, and the number of beds in long-term care homes are included in the fixed effects. To explore the correlation between cases and deaths inside each area and across areas, three bivariate models are considered for the latent effects, namely an independent one, a conditional autoregressive model, and one that allows for both spatially structured and unstructured sources of variability. As the inclusion of spatial effects change some of the fixed effects, we extend the Spatial+ approach to a Bayesian areal set up to investigate the presence of spatial confounding. Results show that the cumulative totals of cases and deaths are negatively correlated inside and across the boroughs of Montreal. The covariates are not associated in a similar manner for the cases and deaths due to COVID-19. The educational level and the median age seem spatially confounded for the cases and deaths across the boroughs of Montreal.