On a method of mortality analysis incorporating age--year interaction, with application to prostate cancer mortality

A model used in the analysis of tabular mortality data (or incidence data), in which deaths are classified by age and year of occurrence, is shown to arise from the assumption that effects due to epoch of birth (the cohort effects) act multiplicatively on an underlying hazard function which may change with calendar year. The model disentangles the cohort effects and the effects due to epoch of death (year effects) and age at death (age effects), and incorporates an age--year interaction which has an interpretation in terms of changing the shape of the underlying hazard function. In addition, the derivation of the hazard function suggests meaningful interpretation of certain combinations of the model parameters. As an illustration, application of the model to prostate cancer mortality in England and Wales indicates, among other things, that after allowing the changing cohort effects, the risk for young men has increased relative to that for older men in recent years.