qPnoMAD: A Residual-Trend-Based, ML-Guided Tool for Automated PopPK Model Development
Undine Falkenhagen1, Zrinka Duvnjak2,3, H. Maxime Lagraauw1, Robin Michelet1, Lars Lindbom1
1qPharmetra LLC, 2Freie Universität Berlin, 3PharMetrX
Introduction: Developing structural models in population pharmacokinetics is a complex and iterative process, traditionally relying on subjective decision-making. Automating the inherent rules and heuristics using machine learning (ML) offers the potential to streamline model development and guide the selection of promising, parsimonious models that retain key pharmacokinetic properties. Objectives: •To evaluate candidate PK model components (e.g., compartments, linear/nonlinear clearance mechanisms, absorption processes, inter-individual variability (IIV) structure) by comparing a set of diagnostic metrics among candidate models. •To develop a Nonlinear Mixed-effects Model Automated Development (qPnoMAD) tool using ML classification algorithms based on diagnostic metrics. •To benchmark the performance of qPnoMAD against an existing Automatic Model Development (AMD) tool implemented in PharmPy [1] . Methods: Our approach defines a search space of 18 structural model components relevant to classical PK models. The stepwise model building approach relies on an ML model to propose the best next step (adding or removing a component from the current candidate model), which is accepted or rejected based on predefined significance cutoffs. As features for the ML model to evaluate the relevance of the model components, 17 diagnostic metrics were derived from: •polynomial fits to the CWRES-vs-time-curve before/after tmax (expected to be informative for absorption/elimination processes), and •the distribution of ETAs (expected to be relevant for IIV components). To create the training data, we simulated datasets from ‘true models’ based on real-world clinical PK datasets, and computed the diagnostic metrics for candidate models from the search space. Multiple ML classification algorithms (e.g., random forest, logistic regression, support vector machine) were considered to rank the candidate models for the next step (deviating in one component from the current model). The classification performance of the ML models was assessed via their accuracy, precision and recall. Performance of the model development was benchmarked against an existing AMD tool based on PharmPy, with comparing computational efficiency and secondary PK parameter-based metrics. The performance was preliminary evaluated on 4 external simulated datasets from published drug-development program models, imitating their corresponding study designs [2,3]. Results: Preliminary analyses based on a random forest classifier demonstrate that the ML model reliably identifies relevant model components, thus efficiently guiding the modelling trail to a fit-for-purpose model. In benchmarking tests, qPnoMAD produced similar final models to those obtained from the PharmPy-based AMD tool but with substantially fewer modelling steps. Although qPnoMAD was generally computationally efficient, run times increased for highly nonlinear models (e.g. with Michaelis-Menten kinetics while still remaining significantly faster than exhaustive search tools. In two small-molecule drug datasets, qPnoMAD identified models with a median deviation of 1.0% and 4.7% for individual predicted Cmax, and 1.5% and 3.1% for AUC from the re-estimated true model secondary parameters, compared to deviations of <2% for the PharmPy-based tool. For two monoclonal antibody datasets, qPnoMAD achieved deviations of 5.9% and 1.4% in Cmax and 1.8% and 0.7% in AUC, compared to deviations of <3% for the PharmPy-based tool. All of these deviations were considered acceptable for the intended model-building purpose. Conclusions: Integrating ML classification algorithms into the structural model development process complements and accelerates traditional manual methods in population pharmacokinetics. By systematically evaluating candidate model components using residual-trend-based diagnostic metrics , qPNoMAD delivers fast, objective, and efficient model selection. In comparison with other automatic methods [1,4] that often use a more exhaustive search (e.g. greedy algorithms), qPNoMAD finds a fit-for-purpose model in a much shorter model trail by leveraging diagnostic metrics that mimic model building heuristics by experienced pharmacometricians. Future work will explore the dependence on model structures and sampling schedules in the training data and validate the approach across more diverse test datasets.
[1] Chen X, Nordgren R, Belin S, et al. A fully automatic tool for development of population pharmacokinetic models. CPT Pharmacometrics Syst Pharmacol. 2024; 13: 1784-1797. doi:10.1002/psp4.13222 [2] Rosario M, Dirks NL, Gastonguay MR, et al. Population pharmacokinetics-pharmacodynamics of vedolizumab in patients with ulcerative colitis and Crohn’s disease. Aliment Pharmacol Ther. 2015; 42(2): 188-202. doi:10.1111/apt.13243 [3] Marathe DD, Jauslin PM, Kleijn HJ, et al. Population pharmacokinetic analyses for belzutifan to inform dosing considerations and labeling. CPT Pharmacometrics Syst Pharmacol. 2023; 12(10): 1499-1510. doi:10.1002/psp4.13028 [4] Li X, Sale M, Nieforth K, et al. pyDarwin: A Machine Learning Enhanced Automated Nonlinear Mixed-Effect Model Selection Toolbox. Clin Pharmacol Ther. 2024; 115: 758-773. doi:10.1002/cpt.3114
