Nonlinear mixed effects (NLME) modeling is a powerful tool to analyze time series data from several individual entities. In this talk, we will give a brief overview of a package for NLME modeling in Mathematica entitled NLMEModeling, implementing the so-called first-order conditional estimation method with sensitivity equation-based gradients for parameter estimation. NLMEModeling supports mixed effects modeling of dynamical systems where the underlying dynamics are described by either ordinary or stochastic differential equations combined with observation expressions with flexible observation error models. Moreover, NLMEModeling is a user-friendly package with functionality for parameter estimation, model validation (such as goodness-of-fit analysis and visual predictive checks) and generation of synthetic data by model simulation.
The package is freely available and provides an extensible add-on for Mathematica users facing the problem of estimating dynamical models given time series data from multiple individuals sharing the same model structure, but with parameters from a population distribution. The package has been applied to challenging problems both in pharmacometrics (clinical and preclinical data) as well as in microbiology (multiple single-cell data).