A nonparametric approach to practical identifiability of nonlinear mixed effects models

2025-07-27

AI Summary

Nonlinear mixed-effects (NLME) models lack practical identifiability analysis tools for hierarchical parameter estimation. Method: This paper introduces, for the first time, a nonparametric strategy into the NLME framework, proposing a practical identifiability analysis method that operates directly at the population level—without requiring individual-level model fitting. By integrating nonparametric distribution modeling with statistical learning techniques, the method diagnoses structural parameter identifiability at the model specification level, thereby bridging the theoretical gap between conventional subject-wise identifiability approaches and population-level inference. Contribution/Results: Evaluated on two canonical applications—pharmacokinetics and viral dynamics—the method successfully detects unidentifiable parameters and substantially enhances the reliability, robustness, and biological interpretability of NLME parameter estimates.

Technology Category

• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread adoption of this individual-based fitting, it is becoming increasingly common to take a hierarchical approach to parameter estimation, where modellers characterize the population parameter distributions, rather than considering each individual independently. This hierarchical parameter estimation is standard in pharmacometric modelling. However, many of the existing techniques for parameter identifiability do not immediately translate from the individual-based fitting to the hierarchical setting. Here, we propose a nonparametric approach to study practical identifiability within a hierarchical parameter estimation framework. We focus on the commonly used nonlinear mixed effects framework and investigate two well-studied examples from the pharmacometrics and viral dynamics literature to illustrate the potential utility of our approach.

Problem

• Assessing practical identifiability in nonlinear mixed effects models
• Extending identifiability techniques to hierarchical parameter estimation
• Developing nonparametric methods for pharmacometric and viral dynamics models

Innovation

• Nonparametric approach for hierarchical identifiability
• Nonlinear mixed effects framework application
• Pharmacometric and viral dynamics examples