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Three novel approaches to structural identifiability analysis in mixed-effects models.

David L I Janzén1, Mats Jirstrand2, Michael J Chappell3

  • 1Department of Systems and Data Analysis, Fraunhofer-Chalmers Centre, Chalmers Science Park, SE-412 88 Gothenburg, Sweden; AstraZeneca RD, SE-431 83 Mölndal, Sweden; School of Engineering, University of Warwick, Coventry CV4 7AL, UK.

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Summary

This study introduces three novel methods for analyzing structural identifiability in mixed-effects models, crucial for accurate biological system interpretation. These methods enable previously impossible analyses for widely used mixed-effects models.

Keywords:
Laplace transformMixed-effects modellingRandom differential equationStructural identifiability

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Area of Science:

  • Mathematical Biology
  • Systems Biology
  • Statistical Modeling

Background:

  • Structural identifiability is key for interpreting parameters in biological models.
  • Ordinary differential equation models have established identifiability methods.
  • Mixed-effects models are vital for sparse data and population variance but lack direct identifiability analysis.

Purpose of the Study:

  • To present and apply three novel methods for structural identifiability analysis in mixed-effects models.
  • To address the gap in identifiability techniques for widely used mixed-effects models.

Main Methods:

  • Repeated measurement approach: Utilizes established statistical theorems.
  • Augmented system approach: Extends mixed-effects models to an extended state-space form.
  • Laplace transform mixed-effects extension: Considers moment invariants of the system's transfer function.

Main Results:

  • The three presented methods were applied to various mixed-effects models.
  • Demonstrated the application, comparison, and contrast of the novel identifiability analysis techniques.

Conclusions:

  • Successfully presented three structural identifiability analysis methods for mixed-effects models.
  • These methods provide new capabilities for analyzing structural identifiability in mixed-effects models, a previously underdeveloped area.