The map comparison problem: tests for the overlap of geographic boundaries

The quality of environmental studies is often compromised by the use of statistics, such as correlation and regression for example, which presuppose a statistical model, linear or otherwise, between two variables. When investigating hypotheses about relationships among geographically distributed variables, an alternative approach is to measure the amount of boundary overlap. Boundaries are geographic zones of rapid change in the intensity of a variable, and are often of scientific interest in their own right. Examples of boundaries include ecotones, genetic hybrid zones, pollution plumes, and the front of the wave of advance of an epidemic. Boundary overlap describes zones where boundaries from two or more variables coincide, and are useful for evaluating epidemiologic hypotheses relating health to environmental exposures. This paper proposes four statistics of boundary overlap, and explores their performance using simulation models and real data describing ozone concentrations and hospital admissions for respiratory conditions. The statistics are found sensitive to different aspects of boundary overlap, and provide an additional diagnostic tool in the analysis of geographically distributed variables. Overlap statistics are expected to come into increasing use as the installed base of geographic information systems increases.