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

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  • Massimo Bilancia
  • Giacomo Demarinis

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:1:p:71-94
    DOI: 10.1007/s10260-013-0241-8
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    References listed on IDEAS

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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    3. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    Cited by:

    1. Jarno Vanhatalo & Scott D. Foster & Geoffrey R. Hosack, 2021. "Spatiotemporal clustering using Gaussian processes embedded in a mixture model," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.

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