Age-Period-Cohort Model

The age-period-cohort (APC) model decomposes variation in a vital rate — mortality, incidence, fertility — into three temporal dimensions: the age of individuals, the calendar period of observation, and the birth cohort to which they belong. It is the standard framework for asking whether a trend reflects how risk changes with age, contemporaneous period influences affecting all ages at once, or generational effects carried by successive cohorts. Its defining technical challenge is that cohort equals period minus age, an exact linear dependence that makes the three sets of linear effects unidentifiable without further assumptions; Holford's 1983 formulation clarified exactly which quantities can and cannot be estimated.