  Spatial clustering detection has a variety of applications in diverse fields,
including identifying infectious disease outbreaks, assessing land use
patterns, pinpointing crime hotspots, and identifying clusters of neurons in
brain imaging applications. While performing spatial clustering analysis on
point process data is common, applications to areal data are frequently of
interest. For example, researchers might wish to know if census tracts with a
case of a rare medical condition or an outbreak of an infectious disease tend
to cluster together spatially. Since few spatial clustering methods are
designed for areal data, researchers often reduce the areal data to point
process data (e.g., using the centroid of each areal unit) and apply methods
designed for point process data, such as Ripley's K function or the average
nearest neighbor method. However, since these methods were not designed for
areal data, a number of issues can arise. For example, we show that they can
result in loss of power and/or a significantly inflated type I error rate. To
address these issues, we propose a generalization of Ripley's K function
designed specifically to detect spatial clustering in areal data. We compare
its performance to that of the traditional Ripley's K function, the average
nearest neighbor method, and the spatial scan statistic with an extensive
simulation study. We then evaluate the real world performance of the method by
using it to detect spatial clustering in land parcels containing conservation
easements and US counties with high pediatric overweight/obesity rates.
