Statistical approaches to model reduction in systems pharmacology

Given the narrow therapeutic window and the large inter-individual variability (IIV) associated with certain drugs, employing a fixed dosing strategy may result in unsafe or ineffective therapy. Model-informed precision dosing (MIPD) can improve efficacy and safety for these drugs by individualising doses based on patient-specific data with a suitable model. Traditionally, pharmacokinetic (PK)/pharmacodynamic (PD) models developed from clinical data, thus depending on the study design and population, have been applied in MIPD. While quantitative systems pharmacology (QSP) models promise better extrapolation capabilities, their complexity often prevents straightforward parameter estimation within MIPD. Model reduction approaches can help develop mechanism-based PK/PD models suitable for MIPD that retain the clinically relevant dynamics from QSP models. Yet, these methods often fail to achieve a level of reduction that renders the models as manageable as classical PK/PD models. Moreover, existing reduction approaches often rely on a single reference parameter set, neglecting that, to predict individual outcomes accurately, the reduced model should approximate the full model well across variability. The objective of this thesis is to develop a model reduction method that allows the derivation of mechanism-based PK/PD models from QSP models in the presence of IIV. This involves (i) considerably reducing complexity while maintaining a physiological interpretation, (ii) efficiently accounting for IIV in the reduction, and (iii) evaluating reduced models to assess their suitability for MIPD. As a case study, we consider anticoagulant treatment with warfarin measured by the international normalised ratio (INR). With the aim of reducing the model complexity to a degree suitable for clinical use, we extend a state variable reduction method to incorporate parameter reduction and simplification of the functional complexity of reaction rates. This combination of multiple reduction methods allows for a higher reduction degree than existing methods while preserving the interpretability. The approach enables us to develop a novel warfarin/INR model from a blood coagulation QSP model. This model considerably simplifies INR simulation under warfarin therapy and allows us to identify a promising biomarker for early INR prediction. We account for IIV by simulating a virtual population with diverse parameter values and evaluating the approximation error across this population during model reduction. To enhance the efficiency of virtual population-based model reduction, we introduce a novel sampling method based on empirical observability Gramians. By identifying dominant parameter directions that govern the variability in responses, the high-dimensional parameter space can be covered efficiently. This approach allows for smaller sample sizes without compromising the robustness of reduced models under parameter variability. Before applying a QSP-derived PK/PD model for MIPD, its predictive performance should be evaluated. We externally evaluate the clinical applicability of our reduced warfarin/INR model using a Bayesian approach, integrating the prior knowledge encoded in the model with individual patient data. Despite not being calibrated with clinical data from warfarin initiation, the accuracy and precision of predictions from our QSP-derived warfarin/INR model are comparable to the current gold-standard approach based on an empirical PK/PD model. The proposed model reduction approach offers an improved rationale for developing mechanism-based PK/PD models for precision dosing by addressing IIV and facilitating biomarker identification. The approach enables improved dosing individualisation with the potential to advance patient safety and therapeutic efficacy, specifically in anticoagulant therapy.