Abstract:
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We consider age-period-cohort (APC) model in social studies and chronic disease epidemiology on an a×p table with single observation in each cell, where rows, columns and diagonals represent age, period and birth cohort. The APC classification regression model suffers from an identifiability problem with multiple estimators having the same fitted values. Here we develop a two-stage smoothing-cohort model to address the identifiability problem. In stage 1, a smoothing cohort model yields a unique estimator with consistent estimation for age and period effects but not cohort effect. In stage 2, a non-contrast constraint is applied to age or period effect with estimates from stage 1. Three constraint selection methods are examined, including the largest ratio of estimates, the smallest variance of the estimate ratio and the smallest variance of linear combination of estimates. Our simulation results based on an a>p data set show that the constraints on period effects outperform those on age effects. The constraint by the smallest variance of the period effect ratio yields the best estimation. We demonstrate our method with SEER cancer mortality data and sociology data.
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