  A common goal in modeling demographic rates is to compare two or more groups.
For ex- ample comparing mortality rates between men and women or between
geographic regions may reveal health inequalities. A popular class of models
for all-cause mortality as well as incidence of specific diseases like cancer
is the age-period-cohort (APC) model. Extending this model to the multivariate
setting is not straightforward because the univariate APC model suffers from
well-known identifiability problems. Often APC models are fit separately for
each strata, and then comparisons are made post hoc. This paper introduces a
stratified APC model to directly assess the sources of heterogeneity in
mortality rates using a Bayesian hierarchical model with matrix-normal priors
that share information on linear and nonlinear aspects of the APC effects
across strata. Computing, model selection, and prior specification are
addressed and the model is then applied to all-cause mortality data from the
European Union.
