We propose a full model-based framework for a statistical analysis of incidence or mortality count data stratified by age, period and space, with specific inclusion of additional cohort effects. The setup will be fully Bayesian based on a series of Gaussian Markov random field priors for each of the components. Additional space-time interactions will be either modelled as space-period or space-cohort effects. Statistical inference is based on efficient algorithms to block update Gaussian Markov random fields, which have recently been proposed in the literature. We illustrate our approach in an analysis of stomach cancer data in West Germany.