A unified approach for assessing heterogeneity in age-period-cohort model parameters using random effects

Age-period-cohort models are a popular tool for studying population-level rates; for example, trends in cancer incidence and mortality. Age-period-cohort models decompose observed trends into age effects that correlate with natural history, period effects that reveal factors impacting all ages simultaneously (e.g. innovations in screening), and birth cohort effects that reflect differential risk exposures that vary across birth years. Methodology for the analysis of multiple population strata (e.g. ethnicity, cancer registry) within the age-period-cohort framework has not been thoroughly investigated. Here, we outline a general model for characterizing differences in age-period-cohort model parameters for a potentially large number of strata. Our model incorporates stratum-specific random effects for the intercept, the longitudinal age trend, and the model-based estimate of annual percent change (net drift), thereby enabling a comprehensive analysis of heterogeneity. We also extend the standard model to include quadratic terms for age, period, and cohort, along with the corresponding random effects, which quantify possible stratum-specific departures from global curvature. We illustrate the utility of our model with an application to metastatic prostate cancer incidence (2004-2013) in non-Hispanic white and black men, using 17 population-based cancer registries in the Surveillance, Epidemiology, and End Results Program.