Spatial Clustering for Inhomogeneous Populations

Abstract

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.

A test for the coincident economic and spatial clustering of business enterprises

“…The casecontrol design of the clustering test allows us to distinguish between general in¯uences on clustering among business establishments (e.g., general locational advantages in urban areas) and industry-or value-chain speci®c processes associated with economic interdependence. An additional contribution of the paper is the unique economic (as opposed to epidemiologic) interpretation of the D function introduced by Cuzick and Edwards (1990) and Diggle and Chetwynd (1991). Even interpreting the results conservatively, the consistency in the pattern of ®ndings is striking.…”

“…One means of accounting for this ®rst order variation in plant locations is to employ a case-control design where the controls act to mimic the background distribution of establishments (Cuzick and Edwards 1990;Diggle and Chetwynd 1991;Kingham et al 1995;Bailey and Gatrell 1995). The sample of manufacturing enterprises is bifurcated into cases and controls based on evidence of signi®cant economic linkages between sectors.…”

The relationship between malignant mesothelioma and an asbestos cement plant environmental risk: a spatial case–control study in the city of Bari (Italy)

“…Raw methods for the detection of clustering in relation to a pre-specified source rely on semi-parametric tests based on the distance of cases and controls from the source: the Cuzick and Edwards (CZ) test (Cuzick and Edwards 1990), for example, is a very simple procedure based on the count of the number of cases within the K nearest cases and controls of the source. Under the null hypothesis of no clustering, the test statistic has an exact hypergeometric distribution: the parameter K is commonly set equal to a fraction of the total sampling dimension (5 or 10%).…”

Spatial clustering of leukemia and type 1 diabetes in children in Denmark

“…We used Cuzick-Edwards' test (Appendix C) [17] as our primary explorative method for evaluating the spatial clustering of cases relative to the spatial distribution of the controls. This statistic counts the number of cases among the k-nearest neighbors of a case and was evaluated using k = 5, 10, and 20 neighbors.…”