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The relation between disease risk and a point source of pollution is usually investigated using distance from the source as a proxy of exposure. The analysis may be based on case-control data or on aggregated data. The definition of the function relating risk of disease and distance is critical, both in a classical and in a Bayesian framework, because the likelihood is usually very flat, even with large amounts of data. In this paper we investigate how the specification of the function relating risk of disease with distance from the source and of the prior distributions on the parameters of the function affects the results when case-control data and Bayesian methods are used. We consider different popular parametric models for the risk distance function in a Bayesian approach, comparing estimates with those derived by maximum likelihood. As an example we have analyzed the relationship between a putative source of environmental pollution (an asbestos cement plant) and the occurrence of pleural malignant mesothelioma in the area of Casale Monferrato (Italy) in 1987-1993. Risk of pleural malignant mesothelioma turns out to be strongly related to distance from the asbestos cement plant. However, as the models appeared to be sensitive to modeling choices, we suggest that any analysis of disease risk around a putative source should be integrated with a careful sensitivity analysis and possibly with prior knowledge. The choice of prior distribution is extremely important and should be based on epidemiological considerations.
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