Irregularly shaped cluster finders frequently end up with a solution consisting of a large zone z spreading through the map, which is merely a collection of the highest valued regions, but not a geographically sound cluster. One way to amenize this problem is to introduce penalty functions to avoid the excessive freedom of shape of z. The compactness penalty K(z) is a function used to reduce the scan value of irregularly shaped clusters, based on its geometric shape. Another penalty is the cohesion function C(z), a measure of the absence of weak links, or underpopulated regions within the cluster which disconnect it when removed. It was mentioned in that such weak links could be responsible for a diminished power of detection in cluster finder algorithms. Methods using those penalty functions present better performance. The geometric compactness is not entirely satisfactory, although, because it has a tendency to avoid potentially interesting irregularly shaped clusters, acting as a low-pass filter. The cohesion function penalty method, although, has slightly less specificity.
Objective
We introduce a novel spatial scan algorithm for finding irregularly shaped disease clusters maximizing simultaneously two objectives: the regularity of shape and the internal cohesion of the cluster.