Density-equalizing Euclidean minimum spanning trees for the detection of all disease cluster shapes

Existing disease cluster detection methods cannot detect clusters of all shapes and sizes or identify highly irregular sets that overestimate the true extent of the cluster. We introduce a graph-theoretical method for detecting arbitrarily shaped clusters based on the Euclidean minimum spanning tree of cartogram-transformed case locations, which overcomes these shortcomings. The method is illustrated by using several clusters, including historical data sets from West Nile virus and inhalational anthrax outbreaks. Sensitivity and accuracy comparisons with the prevailing cluster detection method show that the method performs similarly on approximately circular historical clusters and greatly improves detection for noncircular clusters.