DeepNLME - Conditional Generative Scientific Machine Learning with Applications in Pharmacology

Abstract

Nonlinear mixed-effects (NLME) models are essential for analyzing hierarchical and longitudinal data, particularly in pharmacometrics. This paper presents deep nonlinear mixed effects (DeepNLME) models and applications thereof in the DeepPumas software framework. DeepNLME integrates neural networks with scientific and NLME modeling, where the neural network component enhances flexibility and predictive performance, the scientific component enhances interpretability, generalization ability and data efficiency, and the use of random effects enables capturing unexplained individual variability in hierarchical data. This combination exemplifies what we term (Conditional) Generative Scientific Machine Learning (GenSciML), bridging scientific knowledge, data-driven flexibility, and hierarchical probabilistic modeling with generative capacity. We demonstrate DeepNLME’s efficacy on two practically important tasks: discovery of missing dynamical terms and data-driven covariate modeling. Using synthetic data of drug kinetics and response, we show that a DeepNLME model can fit missing dynamical terms, accurately predict individual time-courses, and generalize to novel dosing regimens when trained on a dataset of only 60 patients. Furthermore, we demonstrate how DeepNLME can be used to fit a covariate model, producing individualized prior distributions conditioned on baseline covariates using a dataset of 300 patients. Our findings highlight DeepNLME’s potential for drug development, personalized medicine, and applications requiring interpretable probabilistic modeling of longitudinal data.