  Spatial scan statistics are well known and widely used methods for the
detection of spatial clusters of events. In the field of spatial analysis of
time-to-event data, several models of scan statistics have been proposed.
However, these models do not take into account the potential intra-unit spatial
correlation of individuals nor a potential correlation between spatial units.
To overcome this problem, we propose here a scan statistic based on a Cox model
with shared frailty that takes into account the spatial correlation between
spatial units. In simulation studies, we have shown that (i) classical models
of spatial scan statistics for time-to-event data fail to maintain the type I
error in the presence of intra-spatial unit correlation, and (ii) our model
performs well in the presence of both intra-spatial unit correlation and
inter-spatial unit correlation. Our method has been applied to epidemiological
data and to the detection of spatial clusters of mortality in patients with
end-stage renal disease in northern France.
