Inference and forecasting in the age-period-cohort model with unknown exposure with an application to mesothelioma mortality

It is of considerable interest to forecast future mesothelioma mortality.  No measures for exposure are available so it is not straight forward to apply a dose-response model.  It is proposed to model the counts of deaths directly using a Poisson regression with an age-period-cohort structure, but without offset.  Traditionally the age-period-cohort is viewed to suffer from an identification problem.  It is shown how to re-parameterize the model in terms of freely varying parameters, so as to avoid this problem.  It is shown how to conduct inference and how to construct distribution forecasts.