Multivariate disease risk mapping: a geostatistical approach

Disease mapping methods for the modeling 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, some of these authors, by explicitly modeling the population density over the region of interest, have considered the (log) standardized relative risk as a Gaussian random field. Here, avoiding the direct modeling of the population density over the region of interest, a different multivariate geostatistical approach to the study of spatial variation of disease risk, which may find application in many real situations, 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. Moreover, the approach proposed allows the study of the spatial distribution of more than one disease at a time.