Using survival analysis to study spatial point patterns in geographical epidemiology

The spatial K-function has become a well accepted method of investigating whether significant clustering can be detected in spatial point patterns. Unlike nearest neighbor-based methods, the K-function approach has the advantage of exploring spatial pattern across a range of spatial scales. However, K-functions still have a number of drawbacks. For instance, although K-functions are based on inter-event distances, they only use a count of the number of point events within successive distance bands. This represents data aggregation and information loss. Secondly, and perhaps more significantly, K-functions are based on a cumulative count of point events with distance. This feature raises the possibility that the investigation of pattern at different scales is compromised by the dependency of any one count to previous counts. This paper proposes a new approach to the analysis of spatial point patterns based upon survival analysis. Although typically used in the temporal domain, there is no reason why survival analysis cannot be applied to any positively-valued, continuous variable as well as time. In this paper, survival analysis is applied to the inter-event distance measures of bivariate spatial point patterns to investigate the 'random labeling' hypothesis. It is shown, through both a controlled data situation and empirical epidemiological applications, that such an approach may be a very useful complement to K-function analysis.