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

Lamiae Azizi 1, 2, * Florence Forbes 2 Senan Doyle 2 Myriam Charras-Garrido 1 David Abrial 1
* Corresponding author
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We recast the disease mapping issue of automatically classifying geographical units into risk classes as a clustering task using a discrete hidden Markov model and Poisson class-dependent distributions. The designed hidden Markov prior is non standard and consists of a variation of the Potts model where the interaction parameter can depend on the risk classes. The model parameters are estimated using an EM algorithm and the mean field approximation. This provides a way to face the intractability of the standard EM in this spatial context, with a computationally efficient alternative to more intensive simulation based Monte Carlo Markov Chain (MCMC) procedures. We then focus on the issue of dealing with very low risk values and small numbers of observed cases and population sizes. We address the problem of finding good initial parameter values in this context and develop a new initialization strategy appropriate for spatial Poisson mixtures in the case of not so well separated classes as encountered in animal disease risk analysis. Using both simulated and real data, we compare this strategy to other standard strategies and show that it performs well in a lot of situations.
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[Research Report] RR-7572, INRIA. 2011
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Lamiae Azizi, Florence Forbes, Senan Doyle, Myriam Charras-Garrido, David Abrial. Spatial risk mapping for rare disease with hidden Markov fields and variational EM. [Research Report] RR-7572, INRIA. 2011. 〈inria-00577793〉

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