Age-space-time CAR models in Bayesian disease mapping.

Mortality counts are usually aggregated over age groups assuming similar effects of both time and region, yet the spatio-temporal evolution of cancer mortality rates may depend on changing age structures. In this paper, mortality rates are analyzed by region, time period and age group, and models including space-time, space-age, and age-time interactions are considered. The integrated nested Laplace approximation method, known as INLA, is adopted for model fitting and inference in order to reduce computing time in comparison with Markov chain Monte Carlo (McMC) methods. The methodology provides full posterior distributions of the quantities of interest while avoiding complex simulation techniques. The proposed models are used to analyze prostate cancer mortality data in 50 Spanish provinces over the period 1986-2010. The results reveal a decline in mortality since the late 1990s, particularly in the age group [65,70), probably because of the inclusion of the PSA (prostate-specific antigen) test and better treatment of early-stage disease. The decline is not clearly observed in the oldest age groups.