Statistical Methods & Applications

, Volume 23, Issue 1, pp 71–94 | Cite as

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

  • Massimo BilanciaEmail author
  • Giacomo Demarinis


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, 1995). 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, 2009). Simulated data and a case study show that the performance of our method is at least comparable to that of Kulldorff–Nagarwalla’s statistic.


Spatial clustering Kulldorff–Nagarwalla’s spatial scan statistic Bayesian statistics Model-based spatial scan statistic Integrated nested Laplace approximation (INLA) 



Massimo Bilancia conceived the study and wrote Sects. 15. Giacomo Demarinis wrote Sect. 7 and software for data analysis. Sections 6 and 8 were written jointly. Both authors read and approved the final manuscript. We wish to thank Claudia Monte, PhD, Department of Physics, University of Bari Aldo Moro, and Maria Rosa Debellis, Department of Basic Medical Sciences, Neuroscience and Sense Organs, University of Bari Aldo Moro, for their support. We would like to extend our gratitude to the valuable reviews and contributions by the two anonymous referees. For a better visualisation, the cartographic map of the province of Foggia shown in Fig. 5 is a simplified version of the original \(\hbox {ESRI}^{\mathrm{TM}}\) shapefile provided by Istat. Some polygons whose geographical boundaries lie entirely within the boundaries of another municipality (enclave) have been deleted, without modifying the spatial contiguity structure. All registered trademarks and trademarks appearing in this paper, respectively identified with symbols \({\circledR }\) or \(^\mathrm{TM}\), are the property of their respective owners. SaTScan\(^\mathrm{TM}\) is a trademark of Martin Kulldorff. The SaTScan\(^\mathrm{TM}\) software was developed under the joint auspices of (i) Martin Kulldorff, (ii) the National Cancer Institute, and (iii) Farzad Mostashari of the New York City Department of Health and Mental Hygiene. A no-charge suite of R functions has been developed for computing the Bayesian cluster detection procedure described in this paper. The code is made available upon request under MIT license.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of Bari Aldo MoroBariItaly
  2. 2.D.A.F.G.—Strategic Control Area, Statistical Analysis and PlanningUniversity of Bari Aldo MoroBariItaly

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