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. 2021 Feb 10;40(3):668-689.
doi: 10.1002/sim.8796. Epub 2020 Nov 18.

A likelihood ratio test on temporal trends in age-period-cohort models with applications to the disparities of heart disease mortality among US populations and comparison with Japan

Wenjiang Fu  1 , Junyu Ding  1 , Kuikui Gao  1 , Shuangge Ma  2 , Lu Tian  3
Affiliations

A likelihood ratio test on temporal trends in age-period-cohort models with applications to the disparities of heart disease mortality among US populations and comparison with Japan

Wenjiang Fu et al. Stat Med. .

Abstract

In this article, we introduce the recently developed intrinsic estimator method in the age-period-cohort (APC) models in examining disease incidence and mortality data, further develop a likelihood ratio (L-R) test for testing differences in temporal trends across populations, and apply the methods to examining temporal trends in the age, period or calendar time, and birth cohort of the US heart disease mortality across racial and sex groups. The temporal trends are estimated with the intrinsic estimator method to address the model identification problem, in which multiple sets of parameter estimates yield the same fitted values for a given dataset, making it difficult to conduct comparison of and hypothesis testing on the temporal trends in the age, period, and cohort across populations. We employ a penalized profile log-likelihood approach in developing the L-R test to deal with the issues of multiple estimators and the diverging number of model parameters. The identification problem also induces overparametrization of the APC model, which requires a correction of the degree of freedom of the L-R test. Monte Carlo simulation studies demonstrate that the L-R test performs well in the Type I error calculation and is powerful to detect differences in the age or period trends. The L-R test further reveals disparities of heart disease mortality among the US populations and between the US and Japanese populations.

Keywords: identification problem; intrinsic estimator; penalized profile likelihood; racial disparities; singular design.

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Conflict of interest statement

CONFLICT OF INTEREST

The authors declare no potential conflict of interests.

Figures

FIGURE 1
FIGURE 1
Illustration of the identification problem with the US heart disease mortality data through plot of age, period, and cohort effect estimates by three constraints, identical age effects of 30 and 35 years old, identical period effects of 1980 and 1985, and identical cohort effects of 1910 and 1915. All three constraints fit the data equally well with a deviance of 1430.34 on 54 df
FIGURE 2
FIGURE 2
Plot of specified age (upper-left panel), period (upper-right panel), and cohort (lower panel) effects in generating simulation study data
FIGURE 3
FIGURE 3
Age, period, and cohort trends and 95% pointwise confidence intervals of heart disease mortality among US white males (left panels) and females (right panels)
FIGURE 4
FIGURE 4
Age, period, and cohort trends and 95% pointwise confidence intervals of heart disease mortality among US black males (left panels) and females (right panels)
FIGURE 5
FIGURE 5
Age, period, and cohort trends and 95% pointwise confidence intervals of heart disease mortality among US other males (left panels) and females (right panels)
FIGURE 6
FIGURE 6
Age, period, and cohort trends and 95% pointwise confidence intervals of heart disease mortality among Japanese males (left panels) and females (right panels)
FIGURE 7
FIGURE 7
Comparison of age, period, and cohort trends of heart disease mortality across US racial populations. Upper-left panel: age trend among males; Upper-middle panel: period trend among males; Upper-right panel: cohort trend among males; Lower-left panel: age trend among females; Lower-middle panel: period trend among females; Lower-right panel: cohort trend among females
FIGURE 8
FIGURE 8
Comparison of age, period, and cohort trends of heart disease mortality between US and Japanese males and females. Upper-left panel: age trend among males; Upper-middle panel: period trend among males; Upper-right panel: cohort trend among males; Lower-left panel: age trend among females; Lower-middle panel: period trend among females; Lower-right panel: cohort trend among females
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