A Bayesian hierarchical model for disease mapping that accounts for scaling and heavy-tailed latent effects

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.