The effects of scale on tests for disease clustering

Surveillance of a large geographic region for 'clusters' of adverse health events, particularly cancers, often involves searching for raised incidence in the vicinity of prespecified putative sources of hazard. For reasons of practicality or of confidentiality, incidence and population data are usually only available aggregated over subregions or 'cells'. The performance of statistical procedures designed to detect the presence of clusters can be highly sensitive to the level of aggregation, that is to the choice of partition of the region into the cells. We investigate this sensitivity in the cases of three recently proposed procedures, namely those of Besag and Newell, Stone, and Waller et al. For illustration, we use leukaemia incidence data for 1978-82 in a region of upstate New York, with inactive hazardous waste sites containing trichloroethylene acting as suspected sources.