In-depth numerical model analysis tools to gain insight into model behavior of large-scale pharmacometric models
Authors: De Witte Wilhelmus , Kulesza Alexander , Schaller Stephan 
Published: February 2025

Introduction: The development and application of pharmacometric models to predict preclinical and clinical studies has become a routine exercise in drug development. However, in-depth analysis to gain insight into the developed models is often lacking. The main tools applied to explore the applied models are individual simulations for smaller models and a (global) sensitivity analysis for larger (QSP or PBPK) models[1]. Occasionally, small (semi-)mechanistic models are thoroughly analyzed mathematically with tools such as a bifurcation analysis[2] or singular perturbation theory[3]. This mathematical analysis is often difficult to scale to large QSP or PBPK models. The current limitations in model analysis tools impairs our understanding of the applied models. Objectives: We aimed to bridge the gap between generic numerical high-level model analysis tools for large models and analytical in-depth model analysis tools for small models, by developing a numerical in-depth model analysis toolbox that can be applied to large models. Methods: The analysis toolbox presented here utilizes the standard sensitivity analysis spider plots as present in the esqlabsR package (v5.1.3) and the ospsuite package (v12.0.0) in R (v4.3.1). Simulation models were created using a whole-body Physiologically-Based Pharmacokinetic model (PK-Sim® v11.2) and extended in MoBi® (v11.2) to include TMDD or PD models. The created models were saved as .pkml files and analyzed in R using dedicated R code for the developed analysis toolbox. Results: The starting point for this analysis was the first extension of a single local sensitivity analysis: a repeated local sensitivity analysis with the impact of a change in parameter value evaluated for the change in summary PK parameters such as AUC, Cmax or half-life. Here we developed a “repeated spider plot”, by repeating the sensitivity analysis for various combinations of other parameters that define relevant scenarios. The next step towards a comprehensive understanding of model behavior was the normalization of the sensitivity for the sensitivity of the previous step in the causal chain, which can be used to identify where the observed sensitivity originates. Finally, we applied the repeated spider plot to a modified model with continuous infusion in multiple compartments to identify rate-limiting steps and conditions as well as the compartments in steady-state. The developed analysis tools were applied to several whole-body PBPK model elements including a combined tissue TMDD-PBPK model and to a simple two-compartment model for comparison. Conclusion: Our study demonstrates how variations on the local sensitivity analysis can provide a comprehensive insight into model behavior of large-scale models. The studied examples demonstrate how these analysis tools reveal rate-limiting steps and in which conditions the potential rate-limiting steps become relevant. Citations: [1] D. Lee, S. Nayak, S.W. Martin, A.C. Heatherington, P. Vicini, F. Hua, A quantitative systems pharmacology model of blood coagulation network describes in vivo biomarker changes in non-bleeding subjects, J. Thromb. Haemost. 14 (2016) 2430–2445. https://doi.org/10.1111/jth.13515.[2] S. Bakshi, E. de Lange, P. van der Graaf, M. Danhof, L. Peletier, Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study, CPT Pharmacomet. Syst. Pharmacol. 5 (2016) 339–351. https://doi.org/10.1002/psp4.12098.[3] L.A. Peletier, J. Gabrielsson, Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification, J. Pharmacokinet. Pharmacodyn. 39 (2012) 429–451. https://doi.org/10.1007/s10928-012-9260-6.