No 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.

In disease mapping, the relative risk of a disease is commonly estimated across different areas within a region of interest. The number of cases in an area is often assumed to follow a Poisson distribution whose mean is decomposed as the product between an offset and the logarithm of the disease's relative risk. The log risk may be written as the sum of fixed effects and latent random effects. The commonly used BYM model further decomposes the latent effects into a sum of independent effects and spatial effects to account for potential overdispersion and a spatial correlation structure among the counts. However, this model suffers from an identifiably issue.The BYM2 model reparametrises the latter by decomposing each latent effect into a weighted sum of independent and spatial effects. We build on the BYM2 model to allow for heavy-tailed latent effects and accommodate potentially outlying risks, after accounting for the fixed effects. We assume a scale mixture structure wherein the variance of the latent process changes across areas and allows for outlier identification. We explore two prior specifications of this scale mixture structure in simulation studies and in the analysis of Zika cases from the 2015-2016 epidemic in Rio de Janeiro. The simulation studies show that, in terms of WAIC and outlier detection, the two parametrisations always perform well compared to commonly used models. Our analysis of Zika cases finds 19 districts of Rio as potential outliers, after accounting for the socio-development index, which may help prioritise interventions.