Spatial Cluster Detection Under Dependent Random Environmental Effects

This paper develops a new approach for the detection of spatial clusters in the presence of random environmental effects and covariates when the observed data consist of counts over a regular grid. Such data are frequently overdispersed and spatially dependent. Overdispersion and spatial dependence must be taken into account in the modeling, otherwise the classical scan statistics method may lead to the detection of false clusters. Therefore, we consider that the observed counts are generated by a Cox process, allowing for overdispersion and spatial correlation. The environmental effects here represents unobserved covariates, as opposed to observed covariates whose observations are used via the link function in the model. These random effects are modeled by means of spatial copula with margins distributed according to a Gamma distribution. We then prove that the counts are dependent and negative binomial and propose a spatial cluster detection test based on data augmentation techniques. It is worth noting that our model also includes the case of independent effects for which the counts are independent and negative binomial. An illustration of these spatial scan techniques is provided by a Black Leaf Streak Disease (BLSD) dataset from Martinique, French West Indies. The comparison of our model with Poisson models, with or without covariates, demonstrates the importance of our approach in avoiding false clusters.