Beschreibung:
<jats:title>Abstract</jats:title><jats:p>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 <jats:italic>k</jats:italic> 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 <jats:italic>c</jats:italic> out of <jats:italic>N</jats:italic> 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 <jats:italic>c</jats:italic> of sampled controls. The observed number of cases is assumed to follow the Poisson‐binomial distribution with hyperparameter <jats:italic>p</jats:italic> modelled as a beta (<jats:italic>c</jats:italic> + 1, <jats:italic>N</jats:italic> ‐ <jats:italic>c</jats:italic> + 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.</jats:p>