Spatial moving average risk smoothing

Abstract

This paper introduces spatial moving average risk smoothing (SMARS) as a new way of carrying out disease mapping. This proposal applies the moving average ideas of time series theory to the spatial domain, making use of a spatial moving average process of unknown order to define dependence on the risk of a disease occurring. Correlation of the risks for different locations will be a function of m values (m being unknown), providing a rich class of correlation functions that may be reproduced by SMARS. Moreover, the distance (in terms of neighborhoods) that should be covered for two units to be found to make the correlation of their risks 0 is a quantity to be fitted by the model. This way, we reproduce patterns that range from spatially independent to long-range spatially dependent. We will also show a theoretical study of the correlation structure induced by SMARS, illustrating the wide variety of correlation functions that this proposal is able to reproduce. We will also present three applications of SMARS to both simulated and real datasets. These applications will show SMARS to be a competitive disease mapping model when compared with alternative proposals that have already appeared in the literature. Finally, the application of SMARS to the study of mortality for 21 causes of death in the Comunitat Valenciana will allow us to identify some qualitative differences in the patterns of those diseases.