Hierarchical Bayesian modelling of spatial age-dependent mortality

Hierarchical Bayesian modelling is considered for the number of age-dependent deaths in different geographic regions. The model uses a conditional binomial distribution for the number of age-dependent deaths, a new family of zero mean Gaussian Markov random field models for incorporating spatial correlations between neighbouring regions, and an intrinsic Gaussian model for including correlations between age-dependent mortality rates. Age-dependent mortality rates are estimated for each region, and approximate credibility intervals based on summaries of samples from the posterior distribution are obtained from Markov chain Monte Carlo simulation. The consequent maps of mortality rates are less variable and smoother than those which would be obtained from naive estimates, and various inferences may be drawn from the results. The prior spatial model includes some of the common conditional autoregressive spatial models used in epidemiology, and so model uncertainty in this family can be accounted for. The methodology is illustrated with an actuarial data set of age-dependent deaths in 150 geographic regions of Hungary. Sensitivity to the prior distributions is discussed, as well as relative risks for certain covariates (males in towns, females in towns, males in villages, females in villages).