We propose two approaches for the spatial analysis of cancer incidence data with additional information on the stage of the disease at time of diagnosis. The two formulations are extensions of commonly used models for multicategorical response data on an ordinal scale. We include spatial and age-group effects in both formulations, which we estimate in a nonparametric smooth way. More specifically, we adopt a fully Bayesian approach based on Gaussian pairwise difference priors where additional smoothing parameters are treated as unknown as well. We argue that the methods are useful in monitoring the effectiveness of mass cancer screening and illustrate this through an application to data on cervical cancer in the former German Democratic Republic. The results suggest that there are large spatial differences in the stage proportions, which indicate spatial variability with respect to the introduction and effectiveness of Pap smear screening programs.