Detection of spatial variation in risk when using CAR models for smoothing relative risks

Abstract

In this paper we derive score tests for spatial independence in mortality or incidence risk in the framework of hierarchical spatial models where different Gaussian Markov random field (MRF) priors are given for modelling the area random effects (specifically, two non-intrinsic Gaussian priors and a convolution Gaussian prior). The techniques used to test the practically relevant and important simplifying hypotheses of an absence of spatial variation in risk will provide a guidance for practitioners to select an adequate model (i.e., a model with an exchangeable-independent-prior, an intrinsic prior, a convolution prior or a non-intrinsic prior, for the area-specific random effects distribution). The proposed methodology is illustrated by analyzing the well-known data set of lip cancer in Scotland and female mortality due to cerebrovascular disease in Navarra, Spain.