Bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields.

The relationship between exposure to environmental chemicals during pregnancy and early childhood development is an important issue that has a spatial risk component. In this context, we have examined mental retardation and developmental delay (MRDD) outcome measures for children in a Medicaid population in South Carolina and sampled measures of soil chemistry (e.g. As, Hg, etc.) on a network of sites that are misaligned to the outcome residential addresses during pregnancy. The true chemical concentration at the residential addresses is not observed directly and must be interpolated from soil samples. In this study, we have developed a Bayesian joint model that interpolates soil chemical fields and estimates the associated MRDD risk simultaneously. Having multiple spatial fields to interpolate, we have considered a low-rank Kriging method for the interpolation that requires less computation than the Bayesian Kriging. We performed a sensitivity analysis for a bivariate smoothing, changing the number of knots and the smoothing parameter. These analyses show that a low-rank Kriging method can be used as an alternative to a full-rank Kriging, reducing the computational burden. However, the number of knots for the low-rank Kriging model needs to be selected with caution as a bivariate surface estimation can be sensitive to the choice of the number of knots.