  Spatial scan statistics are well-known methods for cluster detection and are
widely used in epidemiology and medical studies for detecting and evaluating
the statistical significance of disease hotspots. For the sake of simplicity,
the classical spatial scan statistic assumes that the observations of the
outcome variable in different locations are independent, while in practice the
data may exhibit a spatial correlation. In this article, we use spatial
autoregressive (SAR) models to account the spatial correlation in
parametric/non-parametric scan statistic. Firstly, the correlation parameter is
estimated in the SAR model to transform the outcome into a new independent
outcome over all locations. Secondly, we propose an adapted spatial scan
statistic based on this independent outcome for cluster detection. A simulation
study highlights the better performance of the proposed methods than the
classical one in presence of spatial correlation in the data. The latter shows
a sharp increase in Type I error and false-positive rate but also decreases the
true-positive rate when spatial correlation increases. Besides, our methods
retain the Type I error and have stable true and false positive rates with
respect to the spatial correlation. The proposed methods are illustrated using
a spatial economic dataset of the median income in Paris city. In this
application, we show that taking spatial correlation into account leads to the
identification of more concentrated clusters than those identified by the
classical spatial scan statistic.

Methodology