  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 BYM2 model decomposes 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 propose two prior specifications for this scale mixture
parameter. These are compared through simulation studies and in the analysis of
Zika cases from the first (2015-2016) epidemic in Rio de Janeiro city, Brazil.
The simulation studies show that, in terms of the model assessment criterion
WAIC and outlier detection, the two proposed parametrisations perform better
than the model proposed by Congdon (2017) to capture outliers. In particular,
the proposed parametrisations are more efficient, in terms of outlier
detection, than Congdon's when outliers are neighbours. Our analysis of Zika
cases finds 19 out of 160 districts of Rio as potential outliers, after
accounting for the socio-development index. Our proposed model may help
prioritise interventions and identify potential issues in the recording of
cases.
