  To analyze and project age-specific mortality or morbidity rates
age-period-cohort (APC) models are very popular. Bayesian approaches facilitate
estimation and improve predictions by assigning smoothing priors to age, period
and cohort effects. Adjustments for overdispersion are straightforward using
additional random effects. When rates are further stratified, for example, by
countries, multivariate APC models can be used, where differences of
stratum-specific effects are interpretable as log relative risks. Here, we
incorporate correlated stratum-specific smoothing priors and correlated
overdispersion parameters into the multivariate APC model, and use Markov chain
Monte Carlo and integrated nested Laplace approximations for inference.
Compared to a model without correlation, the new approach may lead to more
precise relative risk estimates, as shown in an application to chronic
obstructive pulmonary disease mortality in three regions of England and Wales.
Furthermore, the imputation of missing data for one particular stratum may be
improved, since the new approach takes advantage of the remaining strata if the
corresponding observations are available there. This is shown in an application
to female mortality in Denmark, Sweden and Norway from the 20th century, where
we treat for each country in turn either the first or second half of the
observations as missing and then impute the omitted data. The projections are
compared to those obtained from a univariate APC model and an extended
Lee--Carter demographic forecasting approach using the proper Dawid--Sebastiani
scoring rule.
