Age-Period-Cohort Models: A Comparative Study of Available Methodologies

doi:10.1016/S0895-4356(99)00033-5

Journal of Clinical Epidemiology

Volume 52, Issue 6, June 1999, Pages 569-583

https://doi.org/10.1016/S0895-4356(99)00033-5 Get rights and content

Abstract

This article compares the estimates produced by a number of solutions to the identifiability problem in age-period-cohort models using a series of disease rates with known structure. The results suggest that only those methods that are based on the estimable functions such as curvatures can be recommended for use in all circumstances. The other common approaches that give parameter estimates that are easier to interpret all have induced bias in the estimates. In particular methods based on the minimization of a penalty function to achieve identifiability are only of use if there is no change in the rates with time. Any drift in the rates tends to be expressed as a cohort-based trend. The methods based on individual records introduce a bias if there is a strong age effect in the direction of a decreasing cohort trend and a compensating increase based on period effects. The nonparametric testing method has little power to detect trends in the rates in small tables but ascribes a strong drift in the rates to both period and cohort trends. With careful interpretation, all methods estimate nonlinear components correctly.

Section snippets

Age-period-cohort models and assumptions

Age-period-cohort models are routinely used in descriptive epidemiology to analyze trends in disease incidence and mortality [1]. They are used as a means of summarizing the information in a two-way table of disease rates classified by age group and time period, such as in Table 1. In this table, the birth cohorts form the diagonals with the oldest cohort at the bottom left-hand corner (individuals aged 80–84 in 1960–1964 were born in 1874–1884), and the youngest cohort at the top right-hand

Indentifiability solutions

There are three broad classes of solutions within the age-period-cohort models other than those that are based on arbitrary linear constraints [15]. The first is based on the use of a penalty function that is minimized to derive the necessary extra linear constraint. Second, there are the methods that rely on having individual records of cases so that a three-way age-period-cohort table can be constructed. Finally, there are the methods that concentrate solely on the estimable functions. A

Data generation methodology

The female population of Scotland over the period 1960 to 1989 for ages 30–84 in 5-year age groups and time periods was used as the basis of the calculation of the expected numbers of cases (Table 1). Two separate methods were used to generate the expected rates. The curvature approach [12] is mathematically correct and can be used to generate the data according to any predefined structure. Specifically, data with age effects similar to those obtained in many cancer sites were generated with

Results

The specified parameter estimates for the calculated data are listed in Table 3 for the two-way tables, based on model 1, and in Table 4 for the individual level approach based on model 2. Initially, simple models are used, and then more complex combinations of parameter values are specified to achieve tables that are representative of features that might be observed in practice. Results for a number of models based on a two-way table only are illustrated in Figure 1, Figure 2, Figure 3. The

Conclusions

In the absence of drift and non linear period and cohort effects the method of Robertson and Boyle [19] gives biased estimates of the Age, Period and Cohort effects in the direction of increasing period effects and decreasing cohort effects and Age incidence curves which are not as steep. These effects are not as severe in the presence of some drift in the rates or some non linear period and cohort effects.

If there is a linear drift, then the Decarli and La Vecchia [18] approach is biased

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Original articlesAge-Period-Cohort Models: A Comparative Study of Available Methodologies

Abstract

Section snippets

Age-period-cohort models and assumptions

Indentifiability solutions

Data generation methodology

Results

Conclusions

J Chronic Dis

Trends in Cancer Incidence and Mortality

Analysing the temporal effects of age, period and cohort

Stat Methods Med Res

The estimation of age, period and cohort effects for vital rates

Biometrics

Cancer risk following a community based programme to prevent cardiovascular diseases

Int J Epidemiol

Incidence of perforated ulcer in western Norway, 1935–1990Cohort- or period-dependent time trends?

Am J Epidemiol

Age-period-cohort analysis of breast cancer mortality

Anticancer Res

Female mortality trends in Spain due to tumours associated with tobacco smoking

Cancer Causes Control

Interactions between birth cohort and urbanisation on gastric cancer mortality in Taiwan

Int J Epidemiol

A comparison of three methods of analysis for age-period-cohort models with application to incidence data on non-Hodgkin’s lymphoma

Int J Epidemiol

Models for temporal variation in cancer rates IIAge-period-cohort models

Stat Med

Original articles
Age-Period-Cohort Models: A Comparative Study of Available Methodologies