Spatio-temporal models with errors in covariates: mapping Ohio lung cancer mortality

In estimating spatial disease patterns, as well as in related assessments of environmental equity, regional morbidity and mortality rate maps are widely used. Hierarchical Bayes methods are increasingly popular tools for creating such maps, since they permit smoothing of the fitted rates toward spatially local mean values, with more unreliable estimates (those arising in low-population regions) receiving more smoothing. In this paper we blend methods for spatial-temporal mapping with those for handling errors in covariates in a single hierarchical model framework. Estimated posterior distributions for the resulting highly-parameterized models are obtained via Markov chain Monte Carlo (MCMC) methods, which also play a key role in our approach to model evaluation and selection. We apply our approach to a data set of county-specific lung cancer rates in the state of Ohio during the period 1968-1988. Our model uses age-adjusted death rates, and incorporates recent information regarding smoking prevalence, population density, and the socio-economic status of the counties. This information is critical to understanding the role played by a certain depleted uranium fuel processing facility on the elevated lung cancer rates in the counties that neighbour it.