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Poisson Regression with Change‐Point Prior in the Modelling of Disease Risk around a Point Source
Author(s) -
Kokki Esa,
Penttinen Antti
Publication year - 2003
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200390042
Subject(s) - statistics , poisson distribution , mathematics , poisson regression , point source , bayesian probability , constant (computer programming) , piecewise , posterior probability , computer science , mathematical analysis , medicine , population , environmental health , optics , physics , programming language
Bayesian estimation of the risk of a disease around a known point source of exposure is considered. The minimal requirements for data are that cases and populations at risk are known for a fixed set of concentric annuli around the point source, and each annulus has a uniquely defined distance from the source. The conventional Poisson likelihood is assumed for the counts of disease cases in each annular zone with zone‐specific relative risk and parameters and, conditional on the risks, the counts are considered to be independent. The prior for the relative risk parameters is assumed to be piecewise constant at the distance having a known number of components. This prior is the well‐known change‐point model. Monte Carlo sampling from the posterior results in zone‐specific posterior summaries, which can be applied for the calculation of a smooth curve describing the variation in disease risk as a function of the distance from the putative source. In addition, the posterior can be used in the calculation of posterior probabilities for interesting hypothesis. The suggested model is suitable for use in geographical information systems (GIS) aimed for monitoring disease risks. As an application, a case study on the incidence of lung cancer around a former asbestos mine in eastern Finland is presented. Further extensions of the model are discussed.