Ilona Blanchard 1, Emmanuelle Comets 2,3, Sarah Zohar 1, Jean-Baptiste Woillard 4,5, Sebastian Benzekry 6,7, Moreno Ursino 1
1 Inserm, Inria, Université Paris Cité, UMRS 1346 (Paris, France ), 2 Univ Rennes, Inserm, EHESP, Irset (Institut de recherche en santé, environnement et travail), UMRS 1085 (Rennes, France ), 3 Université Paris Cité and Université Sorbonne Paris Nord, Inserm, IAME (Paris, France ), 4 Inserm P&T, U1248, Université de Limoges (Limoges , France ), 5 CHU Limoges, Service de Pharmacologie, Toxicologie et Pharmacovigilance (Limoges, France ), 6 COMPutational pharmacology and clinical Oncology, Centre Inria d'Université Côte d'Azur (Marseille, France ), 7 Cancer Research Center of Marseille, Institut Paoli-Calmettes, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105 (Marseille, France )
Introduction
Nonlinear mixed-effects models (NLMEMs) are widely used in model-informed precision dosing (MIPD), particularly in pharmacokinetic–pharmacodynamic (PK/PD) analyses in which individual predictions are used to guide dosing. Multiple plausible PK/PD models may coexist, and exposure and response predictions may be affected by model selection. To address structural uncertainty and improve predictive robustness, including at the individual level, model averaging has been proposed. However, existing individualised approaches [4] have been limited to a single class of NLMEMs, with either the PK or the PD component being addressed separately, while the hierarchical dependency inherent to PK/PD models has not yet been treated.
Objectives
The objective is to develop and evaluate individualised model averaging strategies for joint PK/PD models, where the dependency structure is explicitly accounted for.
Methods
Three individualised model averaging strategies were proposed for candidate joint PK/PD NLMEMs, with differences arising from the way weights are propagated across hierarchical levels. In Method 1, referred to as Global Individual Model Averaging (IMAGlobal), each PK/PD model was treated as a single unit, and identical weights were assigned to PK and PD components, thereby preserving the original structural link. In Method 2, Independent Individual Model Averaging (IMAInd), the components were decoupled, and independent weights were assigned to PK and PD models. It allows each model’s contribution to differ according to its specific performance at each level as does the last method. Method 3, Conditional Individual Model Averaging (IMACond), a hierarchical dependency was introduced whereby the averaged PK profile was used as a fixed input for all candidate PD models, reinstating a link between components. This strategy required re-estimation of PD parameters while maintaining the original population parameters while updating individual estimates. Individual model weights were primarily derived from the individual likelihood.
To mitigate overfitting in sparse-data settings, we also considered a novel individual-level criterion derived from the Stochastic Information Criterion (SIC). The original SIC is defined as the individual log-likelihood penalised by a term proportional to the log-determinant of the Fisher information matrix, thereby incorporating a measure of estimation precision. In our adapted version, the Fisher information matrix was replaced by the posterior variance–covariance matrix of the individual parameter estimates, allowing the penalty term to directly reflect posterior uncertainty at the individual level. The strategies were assessed through a simulation study inspired by tacrolimus, a drug with a narrow therapeutic index and high PK variability. A simulated dataset of 300 individuals per scenario mimicking a real PK/PD study was generated, combining three published PK models ([1], [2], [3]) which shared a common structure but differed in parameter estimates and covariate effects, and three structurally different PD models to form three joint PK/PD models. Concentration and effect profiles were simulated under three scenarios: first, using a single PK/PD model; second, with PK generated from a randomly selected model and PD generated from an independently selected model; and third, with PK and PD generated from distinct mixtures of the three candidate models. Sparse individual data, consisting of four observation time points, were used for individual parameter estimation and model weighting. Predictive performance was evaluated using the relative bias (rBias) of individual concentration and effect trajectories. The methods were compared visually using rBias distributions and quantitatively using paired Wilcoxon tests.
Results
When PK and PD structures were correctly specified (Scenario 1), all approaches performed well with a median relative bias (rBias) near 0%. However, systematic bias emerged when PK and PD originated from mixed models (Scenario 3), where IMAGlobal (Method 1) exhibited a significant positive bias of approximately +7%. In contrast, the IMACond method (Method 3) remained robustly centered (median rBias: -1.1%; IQR: [−5.8%, 4.7%]). In Scenario 2, although IMAInd reduced bias propagation, it suffered from high instability (median rBias: -5.2%; IQR: [−24.1%, 7.3%]), whereas IMACond achieved a superior balance between bias reduction and stability (median rBias: -3.4%; IQR: [−14.9%, 2.9%]). Finally, the adoption of SIC-based weights improved Method 3’s performance in Scenario 3, shifting the median rBias from -3.85% (IQR: [−8.8%, 4.7%]) to -1.10% (IQR: [−5.8%, 4.7%]) without compromising the accuracy observed in simpler scenarios.
Conclusions
Improved predictive performance was achieved with IMACond compared with IMAGlobal or IMAInd. Additional robustness was obtained in sparse-data contexts by penalising parameter uncertainty through an adapted SIC criterion.
References:
[1] Andreu, F., Colom, H., Elens, L. et al. A New CYP3A5*3 and CYP3A4*22 Cluster Influencing Tacrolimus Target Concentrations: A Population Approach. Clin Pharmacokinet 56, 963–975 (2017). https://doi.org/10.1007/s40262-016-0491-3
[2] Andrews, L.M., Hesselink, D.A., van Gelder, T. et al. A Population Pharmacokinetic Model to Predict the Individual Starting Dose of Tacrolimus Following Pediatric Renal Transplantation. Clin Pharmacokinet 57, 475–489 (2018). https://doi.org/10.1007/s40262-017-0567-8
[3] Ogasawara, K., Chitnis, S.D., Gohh, R.Y. et al. Multidrug Resistance-Associated Protein 2 (MRP2/ABCC2) Haplotypes Significantly Affect the Pharmacokinetics of Tacrolimus in Kidney Transplant Recipients. Clin Pharmacokinet 52, 751–762 (2013). https://doi.org/10.1007/s40262-013-0069-2
[4] Uster, D.W., Stocker, S.L., Carland, J.E., Brett, J., Marriott, D.J.E., Day, R.O. and Wicha, S.G. (2021), A Model Averaging/Selection Approach Improves the Predictive Performance of Model-Informed Precision Dosing: Vancomycin as a Case Study. Clin. Pharmacol. Ther., 109: 175-183. https://doi.org/10.1002/cpt.2065
This work is part of the DIGPHAT project which was supported by a grant from the French government, managed by the National Research Agency (ANR), under the France 2030 program, with reference ANR-22-PESN-0017.
Reference: PAGE 34 (2026) Abstr 12088 [www.page-meeting.org/?abstract=12088]
Poster: Methodology - New Modelling Approaches