Age-Period-Cohort Analysis

Age-period-cohort (APC) analysis decomposes variation in disease or mortality rates into three temporal components: the effect of age (biological and accumulated risk), the effect of period (influences hitting everyone alive at a given calendar time, such as a new treatment or a recession), and the effect of cohort (lasting imprints of the conditions into which a birth generation was born). Theodore Holford's 1983 Biometrics paper gave the canonical generalized-linear-model formulation and exposed the method's defining obstacle: because cohort equals period minus age, the three predictors are exactly linearly dependent, so their individual linear slopes cannot be separately identified. A large methodological literature has since proposed constraints, reparameterizations, and estimators to extract whatever the data can legitimately support. Yang, Schulhofer-Wohl, Fu, and Land's 2008 work popularized the intrinsic estimator, a principled choice among the infinitely many fitting solutions. APC analysis is a workhorse of descriptive epidemiology and demography, used to read the temporal fingerprints left on rates of cancer, suicide, obesity, and mortality. Done carefully it separates signal from artifact; done carelessly it manufactures trends that the identification problem makes unknowable.