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ADPO: automatic-differentiation-assisted parametric optimization.

Rong Chen1, Mark Sale2, Alex Mazur2

  • 1Data Sciences Software Division, Certara Inc., 4 Radnor Corporate Center, Suite 350, Radnor, 19087, PA, USA. rong.chen@certara.com.

Journal of Pharmacokinetics and Pharmacodynamics
|September 22, 2025
PubMed
Summary
This summary is machine-generated.

Automatic differentiation (AD) is now in Phoenix NLME 8.6, significantly speeding up pharmacokinetic/pharmacodynamic (PK/PD) model analysis. This new method, automatic-differentiation-assisted parametric optimization (ADPO), reduces computation time by 20-50% compared to traditional approaches.

Keywords:
Automatic differentiationDual numberFOCEFinite differencePK/PDParameter estimation

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Area of Science:

  • Pharmacometrics
  • Computational Science
  • Machine Learning

Background:

  • Accurate derivative computation is crucial for nonlinear mixed-effects modeling.
  • Traditional methods like finite difference can be computationally intensive.
  • Phoenix NLME is a widely used software for pharmacokinetic/pharmacodynamic (PK/PD) analysis.

Purpose of the Study:

  • Introduce automatic differentiation (AD) into Phoenix NLME for enhanced parametric optimization.
  • Evaluate the performance and efficiency of AD-based methods compared to traditional finite difference approaches.
  • Assess the impact of AD on various population PK/PD modeling algorithms.

Main Methods:

  • Implemented AD as 'automatic-differentiation-assisted parametric optimization' (ADPO) in Phoenix NLME 8.6.
  • Applied ADPO to first-order conditional estimation extended least squares (FOCE ELS), Laplacian, and adaptive Gaussian quadrature (AGQ) algorithms.
  • Benchmarked ADPO against finite difference (FD) methods using four PK/PD models and various ODE solvers.

Main Results:

  • ADPO and traditional FOCE ELS (using FD) demonstrated comparable accuracy and robustness.
  • ADPO significantly reduced computation time across all tested ODE solvers, generally by 20% to 50%.
  • A specific case using the voriconazole model showed a 95% reduction in run time with ADPO and the 'auto-detect' ODE solver.

Conclusions:

  • ADPO offers a substantial computational advantage for PK/PD modeling in Phoenix NLME.
  • The 'Fast Optimization' option, enabling ADPO, provides a more efficient alternative to traditional gradient calculation methods.
  • AD implementation represents a significant advancement for accelerating complex pharmacokinetic and pharmacodynamic analyses.