Risk-period-cohort approach for averting identification problems in longitudinal models

In epidemiology, gerontology, human development and the social sciences, age-period-cohort (APC) models are used to study the variability in trajectories of change over time. A well-known issue exists in simultaneously identifying age, period and birth cohort effects, namely that the three characteristics comprise a perfectly collinear system. That is, since age = period−cohort, only two of these effects are estimable at a time. In this paper, we introduce an alternative framework for considering effects relating to age, period and birth cohort. In particular, instead of directly modeling age in the presence of period and cohort effects, we propose a risk modeling approach to characterize age-related risk (i.e., a hybrid of multiple biological and sociological influences to evaluate phenomena associated with growing older). The properties of this approach, termed risk-period-cohort (RPC), are described in this paper and studied by simulations. We show that, except for pathological circumstances where risk is uniquely determined by age, using such risk indices obviates the problem of collinearity. We also show that the size of the chronological age effect in the risk prediction model associates with the correlation between a risk index and chronological age and that the RPC approach can satisfactorily recover cohort and period effects in most cases. We illustrate the advantages of RPC compared to traditional APC analysis on 27496 individuals from NHANES survey data (2005–2016) to study the longitudinal variability in depression screening over time. Our RPC method has broad implications for examining processes of change over time in longitudinal studies.