A Shared-Frailty Spatial Scan Statistic Model for Time-to-Event Data

Spatial scan statistics are well-known methods widely used to detect spatial clusters of events. Furthermore, several spatial scan statistics models have been applied to the spatial analysis of time-to-event data. However, these models do not take account of potential correlations between the observations of individuals within the same spatial unit or potential spatial dependence between spatial units. To overcome this problem, we have developed a scan statistic based on a Cox model with shared frailty and that takes account of the spatial dependence between spatial units. In simulation studies, we found that (i) conventional models of spatial scan statistics for time-to-event data fail to maintain the type I error in the presence of a correlation between the observations of individuals within the same spatial unit and (ii) our model performed well in the presence of such correlation and spatial dependence. We have applied our method to epidemiological data and the detection of spatial clusters of mortality in patients with end-stage renal disease in northern France.