Clustering of disease in population units: an exact test and its asymptotic version

An exact probability test and its asymptotic version are described for testing the hypothesis that clustering of disease observed among population units is likely to have been due to chance alone. The test is based on a scheme for ranking possible arrangements of ill and well persons by degree of clustering, as measured by the sum, over all population units, of the ratio of the number of case pairs in a unit to the size of the unit. The proposed measure of clustering is attractive because increasing segregation of ill and well persons consistently results in a higher index of clustering. The power of the test seems at least as good as that of methods with less attractive clustering measures. The exact version allows analysis of clustering in a small number of population units, while the asymptotic version permits calculations based on larger samples.