Segregation indices for disease clustering

Spatial clustering has important implications in various fields. In particular, disease clustering is of major public concern in epidemiology. In this article, we propose the use of two distance-based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population. We derive the asymptotic distributions of the segregation indices and compare them with other distance-based disease clustering tests in terms of empirical size and power by extensive Monte Carlo simulations. The null pattern we consider is the random labeling (RL) of cases and controls to the given locations. Along this line, we investigate the sensitivity of the size of these tests to the underlying background pattern (e.g., clustered or homogenous) on which the RL is applied, the level of clustering and number of clusters, or to differences in relative abundances of the classes. We demonstrate that differences in relative abundances have the highest influence on the empirical sizes of the tests. We also propose various non-RL patterns as alternatives to the RL pattern and assess the empirical power performances of the tests under these alternatives. We observe that the empirical size of one of the indices is more robust to the differences in relative abundances, and this index performs comparable with the best performers in literature in terms of power. We illustrate the methods on two real-life examples from epidemiology.