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

Abstract

As of July 2021, Montreal is the epicentre of the COVID-19 pandemic in Canada with highest number of deaths. We aim to investigate the spatial distribution of the number of cases and deaths due to COVID-19 across the boroughs of Montreal. To this end, we propose that the cumulative numbers of cases and deaths in the 33 boroughs 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 and across areas, three different 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. We find that the model which includes independent latent effects across boroughs performs the best among the ones considered, there appears to be spatial confounding with the diploma and median age variables, and the correlation between the cases and deaths across and within boroughs is always negative.