Matthias Pierre1,2, Frano Mihaljevic2, Julie Bertrand1
1Université Paris Cité and Université Paris Sorbonne Paris Nord, Inserm, IAME, F-75018 , 2Simulations Plus, CPP software
Introduction: Automated model building is not a new subject, and indeed Bies et al. already proposed a Genetic Algorithm (GA) for this in 2006 [1]. Recently, new tools have been released such as Pharmpy [2] and pyDarwin [3], with Pharmpy using a tree-based algorithm while pyDarwin offers a pool of algorithms. Research evaluating these tools have either compared two algorithms across several datasets or investigated several algorithms on one single dataset [4,5,6,7]. Finally, two other algorithms, Ant Colony Optimization (ACO) and Tabu search, have been compared to a GA [8,9] using simulations. Objectives: To implement six model building automation algorithms using Monolix (1) GA, (2) Particle Swarm Optimization (PSO), (3) Simulated Annealing (SA), (4) ACO, (5) Tournament (TA) and (6) Decision tree (DT), and to evaluate their performance on 200 simulated and 10 real data sets. Methods: First, we performed a simulation study with the PK model and study design inspired from Johannesen et al. [10]: (1) with a lag time, first order absorption, two compartment distribution, a linear elimination and a proportional error model, with an initialization of the parameters based on the data and (2) 22 patients divided in two groups of five sampling times optimized with PopED [11]. All algorithms were run to select the structural PK and residual error model among the 90 possible models (from the Monolix library) on the 100 simulated datasets. Their performance was evaluated in terms of concordance with an exhaustive search and their computing time, as well as accuracy and precision of predicted individual Area under the curve (AUC) and the maximal concentration (Cmax). Second, we performed a simulation study with a Target-Mediated Drug Disposition (TMDD) model with two outputs, the concentration of ligand and receptor, and study design inspired by Budha et al. [12]: (1) with a lag time, first order absorption, two compartment distribution, an irreversible binding approximation and a proportional error model for both outputs with initial parameters fixed for each model and (2) 18 patients divided in three dosing groups with 12 sampling points for the ligand and 6 for the receptor from the real study. Only ACO, TA and DT were run, based on the previous results, to select the structural PK, inter-individual variability, and residual error model for the ligand and receptor among the 230,400 possible models for the 100 simulated datasets. Initial parameters values were fixed for all models. Their performance was evaluated in terms of selecting the model with the lowest fitness function as well as accuracy and precision of predicted individual AUC and Cmax, and the computing time. Finally, we used ACO, TA, and DT to select the structural PK, inter-individual variability, and residual error model for 10 real datasets described in Ayral, G. et al. [13] with varying study designs (dense or sparse) and administration types yielding search spaces of 756 to 15,120 possible models. Results: In the first simulation study, ACO, GA, PSO, TA, and DT provided similar results with >90% concordance with the exhaustive search, with SA being slightly below that, in less than 30 minutes per dataset. Individual predictions were accurate and precise for all algorithms. In the second simulation study, ACO most often found the best model but took approximately 9 hours per dataset, compared to 3 hours for DT. Nevertheless, individual predictions of AUC and Cmax were similar across algorithms, yet less precise for DT. For the 10 real datasets, all three algorithms found models with a lower fitness function than the one used in Ayral, G. et al. [13], with DT most often finding the best model, as defined by lowest cost function. Conclusion: DT appears to be a good solution for search spaces with few possible models. It is outperformed by ACO for a larger search space although ACO comes with a high computing cost.
[1] Bies, R.R. et al., Journal of Pharmacokinetics and Pharmacodynamics (2006) [2] Nordgren, R. et al., PAGE 29 (2021) [3] Li, X. et al., Clinical Pharmacology & Therapeutics (2024) [4] Chen, X. et al., CPT: Pharmacometrics & Systems Pharmacology (2024) [5] Duvnjak, Z. et al., CPT: Pharmacometrics & Systems Pharmacology (2024) [6]Li, X. et al., Journal of Pharmacokinetics and Pharmacodynamics [Preprint] (2024) [7] Huang, Z. et al, PAGE 31. (2023) [8] Huang, Z. et al., PAGE 32 (2024) [9] Richardson, S. et al., Research square [Preprint] (2024) [10] Johannesen, L. et al., Clinical Pharmacology & Therapeutics (2014) [11] Nyberg, J. et al., Computer Methods and Programs in Biomedicine (2012) [12] Budha, N.R. et al., The AAPS Journal (2015) [13] Ayral, G. et al., CPT: Pharmacometrics & Systems Pharmacology (2021)
Reference: PAGE 33 (2025) Abstr 11630 [www.page-meeting.org/?abstract=11630]
Poster: Methodology - New Modelling Approaches