Matthias Pierre 1,2, Frano Mihaljevic 2, Julie Bertrand 1
1 Université Paris Cité and Université Paris Sorbonne Paris Nord, Inserm, IAME (Paris, France), 2 Simulations Plus, PTO (, United States)
Introduction: Automated pharmacokinetic (PK) model building has been explored since 2006, when Bies et al. proposed using a Genetic Algorithm (GA) [1]. Subsequent tools, such as Pharmpy [2] and pyDarwin [3] or mlxModelFinder [4], have been proposed which remain computationally intensive. Machine learning (ML) algorithms are expected to offer a rapid alternative by leveraging patterns learned from prior data rather than running optimization algorithms to be tuned for each dataset. For instance, Sibieude et al. [5] showed that neural network–based algorithms could identify structural PK models ; however, their neural network requires constrained input data and is consequently not applicable to new PK datasets, regardless of their format.
Objectives: This study aimed to (i) construct a database of intravenous pharmacokinetic concentration versus time data, (ii) train two machine learning algorithms—XGBoost [6] and CatBoost [7]—to predict the number of distribution compartments, and (iii) evaluate their performance on real-case study datasets.
Methods: This study relies on several supervised machine-learning algorithms to model the targeted outputs from input data. We considered two tree-based algorithms, namely XGBoost and CatBoost, the latter offering native support for multi-output learning. These algorithms require a training phase using paired input–output examples; consequently, a task-specific database was constructed to ensure consistent learning .
A literature search was thus conducted in PubMed on January 8, 2026, using the keywords “pharmacokinetic*” AND (“infusion” OR “bolus” OR “intravenous” OR “IV”) AND (“one compartment*” OR “1 compartment*”), restricted to human studies published within the last five years. Equivalent searches were performed for two- and three-compartment models.
From each article, population pharmacokinetic model and parameter estimates, residual error model and estimates, and study design characteristics (number of subjects and samples per subject, administered dose, and sampling time interval) were extracted. Using this information, simulations were performed for each article to generate datasets of 100 subjects with 24 evenly spaced samples.
A set of descriptive metrics was extracted from each simulated PK profile to serve as input data to XGBoost, and CatBoost, including for instance the area under the concentration–time curve, the volume of distribution, the number of breakpoints in the log-linear elimination phase (using the Continuous Pruned Optimal Partitioning algorithm [8]), and spline coefficients (using the Least Squares regression applied to B_splines) . The output data was the number of distribution compartments selected via an exhaustive search conducted with Monolix [9]. To ensure comparability across datasets, time and individual concentrations were normalized to their maximum value per dataset.
Additionally, a sensitivity analysis was conducted to evaluate the impact of key algorithmic hyperparameters.
Subsequently, the ML approaches were trained on all generated datasets and applied to data of pharmacokinetic studies on Remifentanil in adults [10] and infants [11], Midazolam [12], M2000 [13], Ascrinvacumab [14] and Tranexamic acid [15].
Results: The search resulted in the inclusion of 123 articles, distributed evenly across one-, two-, and three-compartment models (n = 41 each).
Sensitivity analysis indicated that smaller tree depths improved performance for both XGBoost and CatBoost, and that feature permutation was beneficial for CatBoost.
Each ML approach was trained 100 times using 90% of the generated datasets randomly selected while maintaining equal representation of one-, two-, and three-compartment models, and tested on the remaining 10%. Performance was assessed using balanced accuracy (mean accuracy across compartments) as well as training and testing computation times.
Training times were approximately 5 and 10 seconds for XGboost and CatBoost, while testing times were approximately 0.01 and 0.03 seconds. Balanced accuracy was 71% and 75% for XGboost, and CatBoost, respectively. We also observed that class-specific accuracy differed across compartment models, reaching approximately 80% for one- and three-compartment models and 70% for two-compartment models.
Finally, XGBoost, and CatBoost matched the exhaustive search results in 4/6, and 5/6 case studies, respectively.
Conclusion: We managed to train ML algorithms to rapidly and robustly identify the number of pharmacokinetic distribution compartments. Further evaluations on other real-world datasets are warranted, as well as the algorithm extension to the identification of elimination and absorption processes.
References:
[1] Bies, R.R. et al., Journal of Pharmacokinetics and Pharmacodynamics (2006)
[2] Chen, X. et al., CPT: Pharmacometrics & Systems Pharmacology (2024)
[3] Li, X. et al., Clinical Pharmacology & Therapeutics (2024)
[4] MonolixSuite Documentation, mlxModelFinder (2026)
[5] Sibieude, E. et al., Journal of Pharmacokinetics and Pharmacodynamics (2022)
[6] Chen, T. et al., Knowledge Discovery and Data mining (2016)
[7] Prokhorenkova, L. et al., Neural Information Processing Systems (2018)
[8] Fearnhead, P et al., Journal of Statistical Stoftware (2024)
[9] Simulations Plus, MonolixSuite (2026)
[10] Minto, CF et al., Anesthesiology (1997)
[11] Ross, A et al., Anesthesia & Analgesia (2001)
[12] Wiebe, S et al., Journal of Pharmacokinetics and Pharmacodynamics (2020)
[13] Millard, S et al., Springer New York (2001)
[14] Luu, K et al., Journal of Pharmacology and Experimental Therapeutics (2012)
[15] Lanoiselée, J et al., British Journal of Clinical Pharmacology (2017)
Reference: PAGE 34 (2026) Abstr 11930 [www.page-meeting.org/?abstract=11930]
Poster: Methodology - New Modelling Approaches