Web appendix 1. Results of age-period-cohort analysis

We performed an age-period-cohort analysis to test whether changes in mortality occurring around 2002 were due to cohort- or period-effects. We first fitted a model in which mortality is a function of age and an interaction term of age by year only, thus allowing for different mortality levels by age and for different but constant mortality trends by age. We then introduced a term allowing for a period-effect (a change in trend occurring at a single point in calendar-time affecting all age-groups) or a term allowing for a cohort effect (a change in trend occurring at a single point in the birth-year distribution affecting all age-groups). An optimal calendar year for the period effect and an optimal birth-year for the cohort effect were identified using the Nelder-Mead method as supplied in the “optim” function in the R-package (version 2.7.1).Several initial solutions were tried to avoid local optima.In formula form the models can be represented as follows:

We compared the goodness-of-fit of the age-period and age-cohort models with the age specific drift model on the basis of their scaled deviance. The drop in deviance is caused by additionally estimating parameters gamma and Jstar, ie two degrees of freedom extra.

All analyses were done on a dataset of deaths and person-years at risk by age (in 5-year age-groups, from age 65-69 up to age 95+) and calendar year (1990-2008), using Poisson regression analysis. Analyses were done for males and females separately.

The results of the age-period-cohort analysis (see table) show that the age-period model (allowing for a single period effect) is much better in explaining the mortality data than the age-cohort model (allowing for a single birth-cohort effect). The reduction in scaled deviance (as compared to aage specific drift model) of an age-period model is considerably larger than that of an age-cohort model (and highly statistically significant). For both men and women the model estimate of the point in time at which a period change occurred is between 2001 and 2002. The model estimate for the birth year at which a cohort change occurred differs strongly between men (1928) and women (1916).

Table.

Panel A. Results of age-period-cohort analysis: deviance of models

Men / Women
Deviance of age specific drift model(degrees of freedom) / 1502.8 (119) / 1325.2 (119)
Deviance of age-period model (degrees of freedom) / 393.43 (117) / 357.64 (117)
Change in deviance as compared to null-model (p-value) / 1109.4 (2) p<0.001 / 967.6 (2) p<0.001
Deviance of age-cohort model (degrees of freedom) / 976.48 (117) / 944.15 (117)
Change in deviance as compared to null-model (p-value) / 526.3 (2) p<0.001 / 381.1 (2) p<0.001

Panel B. Results of age-period-cohort analysis: parameter estimates

Men / Women
Period-effect: calendar-year (95% CI) / 2001.5
(2001.31- 2001.73) / 2002.0
(2001.75-2002.17)
Period-effect: change in mortality trend (95% CI) / -0.02759
(-0.02922 --0.02597) / -0.02495
(-0.02652 --0.02337)
Cohort-effect: birth-year (95% CI) / 1928.4
(1928.20 -1928.64) / 1916.4
(1916.08- 1916.64)
Cohort effect: change in mortality trend (95% CI) / -0.03187
(-0.03460--0.02914) / -0.02229
(-0.02453 --0.02005)

Explanation of parameter values for period and cohort effects: if period-effect (gamma) for men is -0.02759, then trend after J* is exp(0.0276) = 0.9728 times trend before J*

References:

Clayton D, Schifflers E. Models for temporal variation in cancer rates. I: Age-Period and Age-Cohort models. Stat Med 1987; 6: 449–67.

Clayton D, Schifflers E. Models for temporal variation in cancerrates. II: Age-Period-Cohort models. Stat Med 1987; 6:469–81.

NelderJA, Mead R. A simplex algorithm for functionminimization. Computer Journal 1965; 7: 308-313.