Some interpolation estimates in environmental risk assessment for spatially misaligned health data

Ecological regression studies are widely used in geographical epidemiology to assess the relationships between health hazard and putative risk factors. Very often health data are measured at an aggregate level because of confidentiality restrictions, while putative risk factors are measured on a different grid, i.e. independent (exposure) variable and response (counts) variable are spatially misaligned. To perform a regression of the risk on the exposure, one needs to realign the spatial support of the variables. Bayesian hierarchical models constitute a natural approach to the problem because of their ability to model the exposure field and the relationship exposure/relative risk on different levels of the hierarchy, taking proper account of the variability induced from the covariate estimation. In this paper we propose two fully Bayesian solutions to the problem. The firs one is based on the kernel smoothing technique, the second one is built on the tessellation of the study region. We illustrate our methods by assessing the relationship between exposure to uranium in drinkable waters and cancer incidence in South Carolina, USA.