Parameter Estimation for Nonlinear Mixed Effects Models Implemented in Mathematica

Conference poster, 2019

In many applications within biology and medicine, measurements are gathered from several entities in the same experiment. This could for example be patients exposed to a treatment or cells measured after stimuli. To characterize the variability in response between entities, the nonlinear mixed effects (NLME) model is a suitable statistical model. An NLME model enables quantification of both within- and between subject variability. The parameter estimation in NLME models is not straightforward, due to the intractable expression of the likelihood function. In this work we present a Mathematica package for parameter estimation in NLME models where the longitudinal model is defined by differential equations. The parameter estimation problem is solved by the first-order conditional estimation (FOCE) method with exact gradients. The package is demonstrated using data from a simulated drug concentration model.