Niccolò D'Agaro 1,2, Elena Righetti 1, Marco Bozza 1,2, Stefano Giampiccolo 1,3, Simone Pezzuto 2, Federico Reali 1
1 Fondazione The Microsoft Research - University of Trento Centre for Computational and Systems Biology (Rovereto, Italy), 2 University of Trento, Department of Mathematics (Povo, Italy), 3 University of Trento, Department of Information Engineering and Computer Science (Povo, Italy)
Background
Quantitative systems pharmacology (QSP) models increasingly support clinical decision-making by integrating mechanistic knowledge with heterogeneous experimental data. Sparse population-level data and model non-identifiability often yield multiple plausible parameterizations, motivating the use of virtual populations (VPops) to represent uncertainty and inter-individual phenotypic variability [1]. Among VPop generation strategies, widely used approaches follow the Allen et al. framework [2], generating large plausible populations (PPops) and selecting VPops to match clinical distributions. In this two-stage workflow, candidate “plausible patients” are first screened to satisfy mechanistic/physiological constraints, and a subset is then selected (e.g., via acceptance–rejection/inclusion) so that the resulting VPop reproduces observed clinical statistics without relying on post-hoc weighting [2]. Recent surrogate/emulation strategies aim to reduce this burden by rapidly pre-screening parameter sets and prioritizing simulator evaluations in promising regions; however, comparative evidence across multiple QSP models and commonly reported VPop metrics remains limited [4]. As model complexity increases and VPop generation becomes more computationally demanding, we benchmarked classical optimization-based methods against surrogate-assisted alternatives across QSP models, focusing on total computational cost.
Methods
Two optimization–based VPop generation approaches—simulated annealing (SA) [2] and Metropolis–Hastings Monte Carlo (MH) [3]—were benchmarked against a surrogate-assisted method (SM) using random search [4]. All methods employed the PPop-to-VPop acceptance–rejection scheme of Allen et al. [2], differing only in PPop generation. Evaluations were performed on three QSP models of increasing complexity—plasma cholesterol regulation [5], colonic motility [6], and Gaucher’s disease type 1 [7]—implemented in MATLAB R2025b. VPop generation methods were compared by established metrics of efficiency, diversity, convergence to empirical target distributions (Kolmogorov–Smirnov (KS) distance on marginal distributions and multivariate energy distance), and computational cost [3]. Unless otherwise stated, results are reported for 10,000 plausible patients. Simulations ran on a MacBook Pro (Apple M2, 16 GB RAM).
Results
Performance varied by model and evaluation metric, revealing recurring trade-offs. In the plasma cholesterol model, MH showed the strongest convergence and highest efficiency, with the lowest runtime (~185 s) versus SM (~934 s) and SA (~2,049 s); SM generated the most diverse VPops. In the colonic motility model, SM delivered a large runtime advantage (~1,517 s vs ~10,886–16,521 s for MH/SA) and the best convergence by multivariate energy distance, whereas MH achieved the lowest KS distance and SA the highest diversity. In the Gaucher’s disease type 1 model, SM again reduced total computational time (~960 s vs ~2,478–2,554 s for MH/SA), produced the most diverse VPops, and achieved convergence close to the best method (KS: 1.36 vs 1.27 for MH; energy distance comparable to SA).
Conclusion
VPop generation in QSP is strongly context-dependent: no single method consistently dominates across models of differing complexity, data characteristics, and outputs. However, the surrogate-assisted strategy—despite surrogate-training overhead—showed a clear benefit in the higher-complexity test cases, markedly reducing runtime and PPop generation time while maintaining competitive convergence and VPop diversity.
References:
1. Cheng, Y. et al. Methods in Molecular Biology (2022) 2486 129–179.
2. Allen, R.J. et al. CPT: Pharmacometrics & Systems Pharmacology (2016) 5(3) 140–146.
3. Rieger, T.R. et al. Progress in Biophysics and Molecular Biology (2018) 139 15–22.
4. Myers, R.C. et al. CPT: Pharmacometrics & Systems Pharmacology (2023) 12(8) 1047–1059.
5. van de Pas, N.C. et al. Journal of Lipid Research (2012) 53(12) 2734–2746.
6. Das, R. et al. Journal of Pharmacokinetics and Pharmacodynamics (2019) 46(5) 485–498.
7. Abrams, R. et al. CPT: Pharmacometrics & Systems Pharmacology (2020) 9(7) 374–383.
Reference: PAGE 34 (2026) Abstr 11935 [www.page-meeting.org/?abstract=11935]
Poster: Methodology - New Modelling Approaches