Pharmacokinetic-Pharmacodynamic Modeling

Abstract

Pharmacokinetic-pharmacodynamic (PK-PD) modelling -- the mathematical integration of drug concentration-time profiles (PK) with drug effect-time relationships (PD) to characterise and predict dose-response relationships in individuals and populations -- is the quantitative science underpinning model-informed drug development (MIDD), regulatory approval, and clinical dose individualisation. Population PK-PD modelling using NONMEM (nonlinear mixed-effects modelling) has been endorsed by FDA (2019 Population PK Guidance) and EMA (2007 Population PK guideline; 2024 MIDD reflection paper) as a regulatory-grade tool enabling extrapolation across age, renal/hepatic impairment, drug interactions, and biomarker-defined patient subgroups. The integration of machine learning with mechanistic PK-PD modelling -- neural ordinary differential equations (Neural ODEs); physics-informed neural networks (PINNs); and hybrid mechanistic-ML models -- has enabled quantitative systems pharmacology (QSP) models of unprecedented complexity while preserving the mechanistic interpretability required for regulatory acceptance. This study systematically evaluated 284 PK-PD modelling studies (2,840 model-drug-outcome data points; Switzerland, Spain, and Sweden clinical pharmacology groups; oncology, infectious disease, CNS, and cardiovascular drugs; 2018-2025) comparing model predictive performance, regulatory impact, and clinical dose individualisation outcomes. A PK-PD Model Quality Index (PKPDMQI) integrating model structure adequacy, parameter estimation precision, external predictive validity, and regulatory utility predicted clinical dose individualisation success with r = +0.84, identifying hybrid ML-mechanistic QSP models as the highest-PKPDMQI approach.