Shape and scale in detecting disease clusters

This dissertation offers a new cluster detection method. This method looks at the cluster detection problem from a new perspective. I change the question of “What do real clusters look like?” to the question of “What do spurious clusters look like?” and “How do spurious clusters affect the ability to recover real clusters?” Spurious clusters can be identified from their geographical characteristics. These are related to the spatial distribution of people at risk, the shape and scale of the geographic units used to aggregate these people, the shape and scale of the spatial configurations that the disease mapping or cluster detection method may impose on the data and the shape and scale of the area of increased risk. The statistical testing process may also create spurious clusters. I propose that the problem of spurious clusters can be resolved using a computational geographic approach. I argue that Monte Carlo simulations can be used to estimate the patterns of spurious clusters in any situation of interest given knowledge of the first three of these four determinants of spurious clusters. Then, given these determinants, where real measurements of disease or mortality are known, it is possible to show those areas of increased risk that are true clusters as opposed to those that are spurious clusters. This distinction is made in a three dimensional signature space, with shape, size and rate as the three axes. The extent of similarity (or dissimilarity) of a cluster to the simulated spurious cluster influences whether it can be recovered. These experiments show that this method is successful in detecting clusters. This method can also predict with reasonable certainty which clusters can be recovered, and which cannot. I compare this method with Rogerson’s Score statistic method. These comparisons expose the weaknesses of Rogerson’s method. Finally these two methods and the Spatial Scan Statistic are applied to searching for possible clusters of prostate cancer incidence in Iowa. The implications of the findings are discussed.