Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)

Among the many tools suited to detect local clusters in group-level data, Kulldorff–Nagarwalla’s spatial scan statistic gained wide popularity (Kulldorff and Nagarwalla in Stat Med 14(8):799–810, <CitationRef CitationID="CR16">1995</CitationRef>). The underlying assumptions needed for making statistical inference feasible are quite strong, as counts in spatial units are assumed to be independent Poisson distributed random variables. Unfortunately, outcomes in spatial units are often not independent of each other, and risk estimates of areas that are close to each other will tend to be positively correlated as they share a number of spatially varying characteristics. We therefore introduce a Bayesian model-based algorithm for cluster detection in the presence of spatially autocorrelated relative risks. Our approach has been made possible by the recent development of new numerical methods based on integrated nested Laplace approximation, by which we can directly compute very accurate approximations of posterior marginals within short computational time (Rue et al. in JRSS B 71(2):319–392, <CitationRef CitationID="CR27">2009</CitationRef>). Simulated data and a case study show that the performance of our method is at least comparable to that of Kulldorff–Nagarwalla’s statistic. Copyright Springer-Verlag Berlin Heidelberg 2014