Density equalizing map projections (cartograms) in public health applications

In studying geographic disease distributions, one normally compares rates among arbitrarily defined geographic subareas (e.g. census tracts), thereby sacrificing some of the geographic detail of the original data. The sparser the data, the larger the subareas must be in order to calculate stable rates. This dilemma is avoided with the technique of Density Equalizing Map Projections (DEMP){copyright}. Boundaries of geographic subregions are adjusted to equalize population density over the entire study area. Case locations plotted on the transformed map should have a uniform distribution if the underlying disease risk is constant. On the transformed map, the statistical analysis of the observed distribution is greatly simplified. Even for sparse distributions, the statistical significance of a supposed disease cluster can be calculated with validity. The DEMP algorithm was applied to a data set previously analyzed with conventional techniques; namely, 401 childhood cancer cases in four counties of California. The distribution of cases on the transformed map was analyzed visually and statistically. To check the validity of the method, the identical analysis was performed on 401 artificial cases randomly generated under the assumption of uniform risk. No statistically significant evidence for geographic non-uniformity of rates was found, in agreement with the original analysis performed by the California Department of Health Services.