Case‐control designs for the detection of spatial clusters of diseases

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.