A CASE STUDY ON POINT PROCESS MODELLING IN DISEASE MAPPING

Viktor Beneš, Karel Bodlák, Jesper Møller, Rasmus Waagepetersen

Abstract

We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis (TBE), and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence of the risk on the covariates. Instead of using the common area level approaches we base the analysis on a Bayesian approach for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using Markov chain Monte Carlo methods. A particular problem which is thoroughly discussed is to determine a model for the background population density. The risk map shows a clear dependency with the population intensity models and the basic model which is adopted for the population intensity determines what covariates influence the risk of TBE. Model validation is based on the posterior predictive distribution of various summary statistics.

Keywords
background intensity; Bayesian estimation; L-function; log Gaussian Cox spatial point process

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DOI: 10.5566/ias.v24.p159-168

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)