Comparison of age-period-cohort models for the analysis of mortality rates

Age\u2013period\u2013cohort (APC) analyses are a family of statistical techniques to study temporal trends in terms of three related time variables: the subject\u2019s age (A), the calendar period (P) and the subject\u2019s birth cohort (C). APC analysis studies the effects of age, period and cohort simultaneously to disentangle their contributions to the studied outcome. The age, period and cohort variables have an exact linear dependence: A=P-C. This causes an identifiability problem. To overcome this issue, three APC analysis methods from the literature are examined. Penalised likelihood APC method This method identifies the solution that minimizes the Euclidean distance between the three two factor models (age-period, age-cohort, cohort-period) by weighing them by their goodness of fit [1]. Generalised additive models (GAM) APC method Carstensen proposed to use natural splines to smooth the non linear curves of APC models using Holford\u2019s parametrization [2]. Partial Least Squares (PLS) APC method PLS regression is used with a two-stage procedure [3]. First a factorial method is applied to obtain the PLS components. These are selected to maximize covariance between the outcome and the unobserved factors. Subsequently the unobserved factors are used as regressors. Finally these coefficients are transformed into the familiar parameters of age, period and cohort. APC analysis is useful to study mortality data, particularly cohort effects, but should be used with caution. Penalised likelihood and GAM methods produce similar results, while the PLS method presents differences. The first two methods use different techniques to distribute the effect of the temporal linear drift between cohort and period factors to solve the identifiability problem, whilst the PLS method solves the problem minimizing the matrix of variances and covariances among the possible estimated parameters in the generalized inverse. From an empirical comparison of the models, we conclude that models based on drift distribution are adequate for epidemiological comparisons, where the problem lies mainly in disentangling the drift effect between cohorts and periods. The PLS model is interesting in projecting future rates. References 1. Decarli A., La Vecchia C. Rivista Statistica Applicata 1987;20:397-410. 2. Carstensen B. Stat Med 2007;26(15):3018-45. 3. Fukuda K. Stat Comp Simulation 2011;81(12):1871\u2013187