Hidde van de Beek 1, Pyry A.J. Välitalo 2,3, J.G. Coen van Hasselt 1, Laura B. Zwep 1
1 Division of Systems Pharmacology and Pharmacy, Leiden Academic Centre for Drug Research, Leiden University (Leiden, the Netherlands), 2 School of Pharmacy, University of Eastern Finland (Kuopio, Finland), 3 Certara Inc (Radnor, USA)
Objectives
Pharmacometric or population modelling traditionally relies on individual level data. Increasingly, previously published models and summary data are recognized as valuable resources for modelling across studies, populations, and sites.
We present and extend a meta-analysis modelling framework developed by our team that enables analysis of both published compartmental population models and extracted aggregate data of PK or PD profiles. The aggregate data modelling (ADM) approach uses either digitized means and variances [1] or data simulated from published population models, advancing the use of model-based meta-analysis (MBMA).
In this presentation we: (1) introduce the aggregate data modelling framework; (2) discuss the development and evaluation of efficient estimation algorithms for the ADM methodology; (3) propose an extended methodology enabling integration of patient covariates, and (4) demonstrate the ADM workflow to a meta-analysis of multiple vancomycin population PK models.
Methods
ADM methodology
The developed ADM methodology uses quasi Monte Carlo (MC) [2] to predict individual time-profiles and summarizes them into the estimated summary metrics ypred and Vpred. The population parameters Ψ are estimated by maximizing the log-likelihood (Eq. 1):
l(Ψ) = log(L(ypred,Vpred│yobs,Vobs)) (1)
An efficient estimation algorithm by iteratively reweighting MC (IR-MC) predictions [3] was subsequently developed and evaluated. Extensive simulation studies were performed to compare the convergence times, bias, and precision for the IR-MC algorithm, for multiple types of models.
The estimation procedure was extended further by incorporating patient covariates associated with primary structural model parameters, by marginalizing the log-likelihood over the distributions of observed summary-level patient covariates.
Application: ADM of vancomycin PK models
We demonstrate the ADM methodology analysis of two published pediatric population PK models for vancomycin [4, 5] . The studies on which these models were based had distinct PK sampling designs (dense[4] or sparse[5]), as well as differences in patient age ranges (age 1-2 years [4] or 2-18 years[5]), which lead to differences in structural and covariate population models. The population PK models developed on these studies were a two-compartmental model [4] and a one-compartmental model [5]. Both models incorporated body weight (BW) as covariates, but were associated with different structural model parameters and corresponding relationships. The two models were implemented using their original study design in rxode2 [6], after which ADM estimation was applied.
Results
ADM methodology
As part of developing the ADM workflow, we first evaluated the computational burden of parameter estimation using an improved iterative reweighting MC algorithm (IR-MC), where changes in parameters reweigh the existing internal predictions. The IR-MC algorithm could accurately estimate the model parameters and improve computational efficiency by up to 100-fold speedups compared to a standard MC algorithm [7].
Integration of covariate modelling was integrated through the log-likelihood (Eq. 1), which is marginalized over the normally distributed covariate distribution A. The following covariate-marginal log-likelihood is generally intractable. As a computationally efficient alternative, we implemented a local approximation approach using a second-order Taylor series (Eq. 2):
l_marg (Ψ) = ∫l(a;Ψ)p(a)da ≈ l(μ;Ψ) + ((σ^2)/2)l”(μ;Ψ) (2)
Application: ADM of vancomycin PK models
The ADM-based meta-analysis of two complementary vancomycin population PK models identified a two-compartmental model population PK model. Differences in study design, structural complexity, and covariate ranges between the source models enabled identification of a single overarching model that predicted both studies well, reducing bias in concentration predictions at Cmax (from 30.5% to 6.7%) and at trough (from 7.8% to 4.4%) compared to cross-prediction between the original models.
Conclusion
We describe the development, evaluation and application of the ADM methodology as a novel meta-analysis framework for analysis of compartmental population models and associated PK or PK/PD data. The ADM methodology enables the estimation of a unified population PK model with interpretable fixed, random, and covariate effects. A fast and accessible version of the ADM method was implemented in the R package “admr”, which facilitates use of rxode2 and C++ for model specification, enabling integration into the pharmacometric modelling ecosystem. Concludingly, this novel method enables integration of diverse published models and aggregate data to arrive at unified and more general population models with broader applicability across studies, designs, and patient populations.
References:
1. Välitalo PAJ (2021) Pharmacometric estimation methods for aggregate data, including data simulated from other pharmacometric models. J Pharmacokinet Pharmacodyn 48:623–638. https://doi.org/10.1007/s10928-021-09760-1
2. Sobol IM (1976) Uniformly distributed sequences with an additional uniform property. USSR Comput Math Math Phys 16:236–242. https://doi.org/10.1016/0041-5553(76)90154-3
3. Levine RA, Casella G (2001) Implementations of the Monte Carlo EM Algorithm. J Comput Graph Stat 10:422–439. https://doi.org/10.1198/106186001317115045
4. Issaranggoon na Ayuthaya S, Katip W, Oberdorfer P, Lucksiri A (2020) Correlation of the vancomycin 24-h area under the concentration-time curve (AUC24) and trough serum concentration in children with severe infection: A clinical pharmacokinetic study. Int J Infect Dis 92:151–159. https://doi.org/10.1016/j.ijid.2019.12.036
5. Alsultan A, Abouelkheir M, Alqahtani S, et al (2018) Optimizing Vancomycin Monitoring in Pediatric Patients. Pediatr Infect Dis J 37:880. https://doi.org/10.1097/INF.0000000000001943
6. Fidler ML, Wang W, Hindmarsh A, et al (2025) rxode2: Facilities for Simulating from ODE-Based Models
7. Aggregate data modelling: A fast implementation for fitting pharmacometrics models to summary-level data in R | Journal of Pharmacokinetics and Pharmacodynamics | Springer Nature Link. https://link.springer.com/article/10.1007/s10928-025-10011-w.
Reference: PAGE 34 (2026) Abstr 12307 [www.page-meeting.org/?abstract=12307]
Poster: Methodology - New Modelling Approaches