Bias-Corrected Least Squares (BCLS) Method for Estimating Parameters in Nonlinear Ordinary Differential Equations Models with Mixed-Effects

Abstract

Ordinary Differential Equation (ODE) is a popular framework for modeling temporal dynamics in a variety of scientific settings. When repeated measurements are available for the dynamic process, it is of great interest to estimate random effects in the ODE model for the process. Current algorithms for parameter estimation in the nonlinear mixed-effects model are often challenging due to intensive computation and slow convergence; while alternative methods mostly rely on smoothing spline functions and therefore a careful choice of smoothing parameters. We propose an extension of the original Bias-Corrected Least Squares (BCLS) method, referred to as BCLS-LME, which reduces the nonlinear mixed-effects model to a linear mixed-effects model that does not require any smoothing. We demonstrate that, using both simulated data and an actual birth cohort data and with proper sampling schemes, the BCLS-LME method achieves comparable accuracy with the NLME method for estimating both ODE parameters and random effects; however, it dramatically improves the computational efficiency by reducing computation time and alleviating convergence difficulties. Given proper sampling schemes and further fine-tuning, the BCLS-LME method is likely to provide a powerful tool for parameter estimation in complex ODE mixed-effects models.