Disease risk mapping: a multivariate geostatistical approach

Disease mapping methods for the modelling of spatial variation in disease rates, to smooth the extreme raw rates in small areas by using information from neighboring areas, has so far almost entirely been concerned with random-effects models embodying some sort of Markov random field structure. These models consider the distribution of the relative risk of an area conditional on that of its neighbors. Typically, two areas are viewed as neighbors if they share a common boundary, regardless of their relative position, size and shape. In recent years, following a geostatistical approach, some authors have advocated more realistic models in which the spatial autocorrelation structure of the disease counts is derived through an underlying risk varying smoothly over the entire region of interest. In particular, by explicitly modelling the population density over the region of interest, these authors have considered (log) standardized relative risk as a Gaussian random field. In this work, avoiding the direct modelling of the population density over the region of interest, a different geostatistical approach to the study of spatial variation of disease risk is proposed. Our approach assumes that the raw data are available not, as in the usual practice, in the form of aggregate counts within sets of disjoint politically defined areas, but in a pointwise "geostatistical" fashion. Extending the proposal made in the literature for the univariate case, which just consider non standardized (by age, sex, etc.) risk, in this work we present an approach to disease mapping based on a hierarchical multivariate spatial model in which the latent structure is given by a Gaussian geostatistical factor model. The methodology proposed is shown on an epidemiological data set coming from an extensive survey on diabetes mellitus in Umbria (Italy).