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.

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.

Sensitivity analysis and parameter identification of nonlinear hybrid systems for glycerol transport mechanisms in continuous culture.

In this paper, we establish a modified fourteen-dimensional nonlinear hybrid dynamic system with genetic regulation to describe the microbial continuous culture, in which we consider that there are three possible ways for glycerol to pass the cell's membrane and one way for 1,3-PD (passive diffusion and active transport). Then we discuss the existence, uniqueness, continuous dependence of solutions and the compactness of the solution set. We construct a global sensitivity analysis approach to reduce the number of kinetic parameters. In order to infer the most reasonable transport mechanism of glycerol, we propose a parameter identification model aiming at identifying the parameter with higher sensitivity and transport of glycerol, which takes the robustness index of the intracellular substance together with the relative error between the experimental data and the computational values of the extracellular substance as a performance index. Finally, a parallel algorithm is applied to find the optimal transport of glycerol and parameters.