Hierarchical models for mapping Ohio lung cancer rates

The mapping of geographical variation in disease occurrence plays an important role in assessing environmental justice (i.e. the equitable sharing of adverse effects of pollution across socio-demographic subpopulations). Bayes and empirical Bayes methods can be used to obtain stable small-area estimates while retaining geographic and demographic resolution. In this study, we focus on modelling spatial patterns of disease rates, incorporating demographic variables of interest such as gender and race. We employ a Bayesian hierarchical modelling approach, which uses a Markov chain Monte Carlo computational method to obtain the joint posterior distribution of the model parameters. We use this approach to construct smoothed maps of lung cancer mortality in Ohio counties in 1988. Our approach also facilitates a cross-validatory comparison between the normal and Poisson likelihoods often fit uncritically to data of this type. Finally, we uncover evidence of changing spatial structure in the rates over the 21-year period 1968 1988, suggesting a spatio-temporal hierarchical model as a new possibility.