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

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.Nous abordons la cartographie automatique d' unités géographiques en classes de risque comme un problème de clustering à l'aide de modèles de Markov cachés discrets et de modèles de mélange de Poisson. Le modèle de Markov caché proposé est une variante du modèle de Potts, où le paramètre d'interaction dépend des classes de risque. Afin d'estimer les paramètres du modèle, nous utilisons l'algorithme EM combiné à une approche variationnelle champ-moyen. Cette approche nous permet d'appliquer l'algorithme EM dans un cadre spatial et présente une alternative efficace aux méthodes d'estimation basées sur des simulations intensives de type Markov chain Monte Carlo (MCMC). Nous abordons également les problèmes d'initialisation, spécialement quand les taux de risque sont petits (cas des maladies animales). Nous proposons une nouvelle stratégie d'initialisation appropriée aux modèles de mélange de Poisson quand les classes sont mal séparées. Pour illustrer notre méthodologie, nous présentons des résultats d'application sur des données épidémiologiques réelles et simulées et montrons la performance de la stratégie d'initialisation présentée en comparaison à celles utilisées usuellement

Anthropogenic factors and the risk of highly pathogenic avian influenza H5N1: prospects from a spatial-based model

Beginning in 2003, highly pathogenic avian influenza (HPAI) H5N1 virus spread across Southeast Asia, causing unprecedented epidemics. Thailand was massively infected in 2004 and 2005 and continues today to experience sporadic outbreaks. While research findings suggest that the spread of HPAI H5N1 is influenced primarily by trade patterns, identifying the anthropogenic risk factors involved remains a challenge. In this study, we investigated which anthropogenic factors played a role in the risk of HPAI in Thailand using outbreak data from the “second wave” of the epidemic (3 July 2004 to 5 May 2005) in the country. We first performed a spatial analysis of the relative risk of HPAI H5N1 at the subdistrict level based on a hierarchical Bayesian model. We observed a strong spatial heterogeneity of the relative risk. We then tested a set of potential risk factors in a multivariable linear model. The results confirmed the role of free-grazing ducks and rice-cropping intensity but showed a weak association with fighting cock density. The results also revealed a set of anthropogenic factors significantly linked with the risk of HPAI. High risk was associated strongly with densely populated areas, short distances to a highway junction, and short distances to large cities. These findings highlight a new explanatory pattern for the risk of HPAI and indicate that, in addition to agro-environmental factors, anthropogenic factors play an important role in the spread of H5N1. To limit the spread of future outbreaks, efforts to control the movement of poultry products must be sustained

Extreme Value Analysis : an Introduction

National audienceWe provide an overview of the probability and statistical tools underlying the extreme value theory, which aims to predict occurrence of rare events. Firstly, we explain that the asymptotic distribution of extreme values belongs, in some sense, to the family of the generalised extreme value distributions which depend on a real parameter, called the extreme value index. Secondly, we discuss statistical tail estimation methods based on estimators of the extreme value index

Extreme Value Analysis : an Introduction

National audienceWe provide an overview of the probability and statistical tools underlying the extreme value theory, which aims to predict occurrence of rare events. Firstly, we explain that the asymptotic distribution of extreme values belongs, in some sense, to the family of the generalised extreme value distributions which depend on a real parameter, called the extreme value index. Secondly, we discuss statistical tail estimation methods based on estimators of the extreme value index

Correctif à l’article : Introduction à l’analyse des valeurs extrêmes

International audienceWe provide an overview of the probability and statistical tools underlying the extreme value theory, which aims to predict occurrence of rare events. Firstly, we explain that the asymptotic distribution of extreme values belongs, in some sense, to the family of the generalised extreme value distributions which depend on a real parameter, called the extreme value index. Secondly, we discuss statistical tail estimation methods based on estimators of the extreme value indexNous donnons un aperçu des résultats probabilistes et statistiques utilisés dans la théorie des valeurs extrêmes, dont l’objectif est de prédire l’occurrence d’événements rares. Dans la première partie de l’article, nous expliquons que la distribution asymptotique des valeurs extrêmes appartient, dans un certain sens, à la famille des distributions des valeurs extrêmes généralisées qui dépendent d’un paramètre réel, appelé l’indice de valeur extrême. Dans la seconde partie, nous discutons des méthodes d’évaluation statistiques des queues basées sur l’estimation de l’indice des valeurs extrême

Correctif à l’article : Introduction à l’analyse des valeurs extrêmes

International audienceWe provide an overview of the probability and statistical tools underlying the extreme value theory, which aims to predict occurrence of rare events. Firstly, we explain that the asymptotic distribution of extreme values belongs, in some sense, to the family of the generalised extreme value distributions which depend on a real parameter, called the extreme value index. Secondly, we discuss statistical tail estimation methods based on estimators of the extreme value indexNous donnons un aperçu des résultats probabilistes et statistiques utilisés dans la théorie des valeurs extrêmes, dont l’objectif est de prédire l’occurrence d’événements rares. Dans la première partie de l’article, nous expliquons que la distribution asymptotique des valeurs extrêmes appartient, dans un certain sens, à la famille des distributions des valeurs extrêmes généralisées qui dépendent d’un paramètre réel, appelé l’indice de valeur extrême. Dans la seconde partie, nous discutons des méthodes d’évaluation statistiques des queues basées sur l’estimation de l’indice des valeurs extrême

Spatio temporal risk mapping based on hidden Markov random fields and variational approximations

International audienc

Hidden Markov random field for spatial and spatial-temporal risk mapping

International audienc