The Annals of Applied Statistics

Spatial risk mapping for rare disease with hidden Markov fields and variational EM

Florence Forbes, Myriam Charras-Garrido, Lamiae Azizi, Senan Doyle, and David Abrial

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Current risk mapping models for pooled data focus on the estimated risk for each geographical unit. A risk classification, that is, grouping of geographical units with similar risk, is then necessary to easily draw interpretable maps, with clearly delimited zones in which protection measures can be applied. As an illustration, we focus on the Bovine Spongiform Encephalopathy (BSE) disease that threatened the bovine production in Europe and generated drastic cow culling. This example features typical animal disease risk analysis issues with very low risk values, small numbers of observed cases and population sizes that increase the difficulty of an automatic classification. We propose to handle this task in a spatial clustering framework using a nonstandard discrete hidden Markov model prior designed to favor a smooth risk variation. The model parameters are estimated using an EM algorithm and a mean field approximation for which we develop a new initialization strategy appropriate for spatial Poisson mixtures. Using both simulated and our BSE data, we show that our strategy performs well in dealing with low population sizes and accurately determines high risk regions, both in terms of localization and risk level estimation.

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Ann. Appl. Stat., Volume 7, Number 2 (2013), 1192-1216.

First available in Project Euclid: 27 June 2013

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Classification discrete hidden Markov random field disease mapping Poisson mixtures Potts model variational EM


Forbes, Florence; Charras-Garrido, Myriam; Azizi, Lamiae; Doyle, Senan; Abrial, David. Spatial risk mapping for rare disease with hidden Markov fields and variational EM. Ann. Appl. Stat. 7 (2013), no. 2, 1192--1216. doi:10.1214/13-AOAS629.

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Supplemental materials

  • Supplementary material: Supplement to “Spatial risk mapping for rare disease with hidden Markov fields and variational EM”. Missing appendices, tables and figures are available in a companion supplemental file.