Disease cluster statistics for imprecise space-time locations

Health professionals are investigating an increasing number of possible disease clusters, and statistical tests play an important role in cluster description and analysis. Existing cluster statistics assume precise data, when in reality health events are often imprecise (for example, place of residence is known only to the census district or zip code) and uncertain (for example, 'I first became ill sometime in 1985'). This incompatibility--precise methods used to analyse imprecise data--is largely ignored, resulting in test statistics of unknown accuracy. Most cluster statistics can be written as the cross-product of two matrices where one matrix reflects nearest-neighbour, distance or adjacency relationships and the second matrix is health related (for example, case-control identities). This paper explores a general approach to clustering, which incorporates uncertainty regarding space-time locations into these nearest neighbour, distance or adjacency relationships. Because the approach is general it can be used with almost all existing cluster tests, and, because it accounts for imprecise location data, it is suited to the 'real-world' nature of disease cluster investigations.