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.

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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.