The Estimation of Age, Period and Cohort Effects for Vital Rates

In models for vital rates which include effects due to age, period and cohort, there is aliasing due to a linear dependence among these three factors. This dependence arises both when age and period intervals are equal and when they are not. One solution to the dependence is to set an arbitrary constraint on the parameters. Estimable functions of the parameters are invariant to the particular constraint applied. For evenly spaced intervals, deviations from linearity are estimable but only a linear function of the three slopes is estimable. When age and period intervals have different widths, further aliasing occurs. It is assumed that the number of deaths in the numerator of the rate equation has a Poisson distribution. The calculations are illustrated with data on mortality from prostate cancer among nonwhites in the U.S.