Letters to the Editor RE: ‘‘BAYESIAN PROJECTIONS: WHAT ARE THE EFFECTS OF EXCLUDING DATA FROM YOUNGER AGE GROUPS?’’ Baker and Bray

Baker and Bray (1) continue Bray’s thoughtful development of a particular Bayesian age-period-cohort model for cancer rate projections. This model has an elegant formulation and has brought to the forefront a Bayesian interpretation of cancer projections. However, we feel that there are more appropriate models for cancer rate projections. Why? The Bayesian age-period-cohort model suffers from very wide credible intervals for predictions outside observed data (2), which can be attributed to the choice of model priors. Although the second-order autoregressive priors for the age, period, and cohort effects are flexible, alternative priors allow for realistic projections with considerably improved precision. Predictive performance can be measured by splitting observed data into a training data set and a test data set (3, 4). The model is fitted with the training data set, and then the deviance or another loss criterion is calculated for predictions on the test data. Taking a Bayesian perspective, we can calculate 1) the plug-in deviance, which is the deviance of the mean predicted values, and 2) the predictive deviance,