  Disease mapping analyses the distribution of several diseases within a
territory. Primary goals include identifying areas with unexpected changes in
mortality rates, studying the relation among multiple diseases, and dividing
the analysed territory into clusters based on the observed levels of disease
incidence or mortality. In this work, we focus on detecting spatial mortality
clusters, that occur when neighbouring areas within a territory exhibit similar
mortality levels due to one or more diseases. When multiple death causes are
examined together, it is relevant to identify both the spatial boundaries of
the clusters and the diseases that lead to their formation. However, existing
methods in literature struggle to address this dual problem effectively and
simultaneously. To overcome these limitations, we introduce Perla, a
multivariate Bayesian model that clusters areas in a territory according to the
observed mortality rates of multiple death causes, also exploiting the
information of external covariates. Our model incorporates the spatial data
structure directly into the clustering probabilities by leveraging the
stick-breaking formulation of the multinomial distribution. Additionally, it
exploits suitable global-local shrinkage priors to ensure that the detection of
clusters is driven by concrete differences across mortality levels while
excluding spurious differences. We propose an MCMC algorithm for posterior
inference that consists of closed-form Gibbs sampling moves for nearly every
model parameter, without requiring complex tuning operations. This work is
primarily motivated by a case study on the territory of the local unit ULSS6
Euganea within the Italian public healthcare system. To demonstrate the
flexibility and effectiveness of our methodology, we also validate Perla with a
series of simulation experiments and an extensive case study on mortality
levels in U.S. counties.
