Spatial Clustering for Inhomogeneous Populations

SUMMARY A new method for detecting spatial clustering of events in populations with non-uniform density is proposed. The method is based on selecting controls from the population at risk and computing interpoint distances for the combined sample. Nonparametric tests are developed which are based on the number of cases among the k nearest neighbours of each case and the number of cases nearer than the k nearest control. The performance of these tests is evaluated analytically and by simulation and the method is applied to a data set on the locations of cases of childhood leukaemia and lymphoma in a defined geographical area. In particular the impact on power of the choice of k and of the ratio of cases to controls is examined. Modifications of the procedure to study distances from predefined objects, to match for known risk factors which would produce unwanted clustering and issues related to estimation are also discussed.