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Case‐control designs for the detection of spatial clusters of diseases
Author(s) -
Biggeri Annibale,
Marchi Marco
Publication year - 1995
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.3170060407
Subject(s) - poisson distribution , statistics , mathematics , negative binomial distribution , context (archaeology) , bayesian probability , cluster analysis , combinatorics , geography , archaeology
To detect spatial clusters of rare diseases, an extension of the method proposed by Besag and Newell to the context of case‐control sampling is presented. For each case location a circle containing at least k other disease cases is drawn. For each circle, the probability of type I error, under the null hypothesis of no clustering, is computed with the Poisson formula with parameter given by the product of the case‐control ratio times the number c out of N controls classified within the circle. In the paper a hierarchical Bayesian formulation of the problem is used to cope with the variability in the number c of sampled controls. The observed number of cases is assumed to follow the Poisson‐binomial distribution with hyperparameter p modelled as a beta ( c + 1, N ‐ c + 1) random variate. A case‐control study on lung cancer in the River Serchio Valley 1987–90 (Tuscany, Italy) exemplifies the method. Statistically significant clusters of cases were found in the vicinity of a copper foundry.