Computer Simulation of Nonlinear Mixed-Effect Models with Ordinary Differential Equations for Genetic Regulation

Nonlinear mixed-effect model is a powerful tool to analyze complex data that have both within-subject and between-subject variabilities. Although a variety of studies have been conducted to infer parameter distributions under the assumption of parameter independence, it is not clear what are the influence of parameter correlation on the system dynamics. In this work we provide computer simulations of nonlinear mixed-effect model with ordinary differential equations. Using a gene network model as the test problem, we examine the influence of parameter correlation on the system dynamics of nonlinear mixed-effect model with normal or nonnormal random effects. Computer simulations show that the increase of positive correlation will elevate the difference between simulations with and without parameter correlation for both normal and gamma random effects. In addition, the increase of negative correlation will enhance the difference between simulations with and without parameter correlation for gamma random effects. However, the increase of negative correlation will decrease the difference between simulations with and without parameter correlation for the normal random effects. Simulation results will provide insights for the inference of parameter distributions under the assumption of parameter correlation.