Managing distance and covariate information with point-based clustering.

BACKGROUND: Geographic perspectives of disease and the human condition often involve point-based observations and questions of clustering or dispersion within a spatial context. These problems involve a finite set of point observations and are constrained by a larger, but finite, set of locations where the observations could occur. Developing a rigorous method for pattern analysis in this context requires handling spatial covariates, a method for constrained finite spatial clustering, and addressing bias in geographic distance measures. An approach, based on Ripley's K and applied to the problem of clustering with deliberate self-harm (DSH), is presented. METHODS: Point-based Monte-Carlo simulation of Ripley's K, accounting for socio-economic deprivation and sources of distance measurement bias, was developed to estimate clustering of DSH at a range of spatial scales. A rotated Minkowski L1 distance metric allowed variation in physical distance and clustering to be assessed. Self-harm data was derived from an audit of 2 years' emergency hospital presentations (n = 136) in a New Zealand town (population ~50,000). Study area was defined by residential (housing) land parcels representing a finite set of possible point addresses. RESULTS: Area-based deprivation was spatially correlated. Accounting for deprivation and distance bias showed evidence for clustering of DSH for spatial scales up to 500 m with a one-sided 95 % CI, suggesting that social contagion may be present for this urban cohort. CONCLUSIONS: Many problems involve finite locations in geographic space that require estimates of distance-based clustering at many scales. A Monte-Carlo approach to Ripley's K, incorporating covariates and models for distance bias, are crucial when assessing health-related clustering. The case study showed that social network structure defined at the neighbourhood level may account for aspects of neighbourhood clustering of DSH. Accounting for covariate measures that exhibit spatial clustering, such as deprivation, are crucial when assessing point-based clustering.

An unsupervised classification method for inferring original case locations from low-resolution disease maps.

BACKGROUND: Widespread availability of geographic information systems software has facilitated the use of disease mapping in academia, government and private sector. Maps that display the address of affected patients are often exchanged in public forums, and published in peer-reviewed journal articles. As previously reported, a search of figure legends in five major medical journals found 19 articles from 1994-2004 that identify over 19,000 patient addresses. In this report, a method is presented to evaluate whether patient privacy is being breached in the publication of low-resolution disease maps. RESULTS: To demonstrate the effect, a hypothetical low-resolution map of geocoded patient addresses was created and the accuracy with which patient addresses can be resolved is described. Through georeferencing and unsupervised classification of the original image, the method precisely re-identified 26% (144/550) of the patient addresses from a presentation quality map and 79% (432/550) from a publication quality map. For the presentation quality map, 99.8% of the addresses were within 70 meters (approximately one city block length) of the predicted patient location, 51.6% of addresses were identified within five buildings, 70.7% within ten buildings and 93% within twenty buildings. For the publication quality map, all addresses were within 14 meters and 11 buildings of the predicted patient location. CONCLUSION: This study demonstrates that lowering the resolution of a map displaying geocoded patient addresses does not sufficiently protect patient addresses from re-identification. Guidelines to protect patient privacy, including those of medical journals, should reflect policies that ensure privacy protection when spatial data are displayed or published.