Leveraging Two-Stage δ Global Sensibility Analysis Method to Inform Parameter Estimation in PBPK Models

Appropriately performing Global Sensitivity Analysis (GSA) and refining models through the estimation of key parameters on individual data are fundamental steps in PBPK modeling, yet they remain insufficiently addressed in current practice. The main aim of this work is to establish a computational framework linking PhysPK with Python, enabling the application of the Two-stage δ GSA and individual parameter estimation via the iterative two-stage (ITS) method to the semi-mechanistic PBPK model Phys-DAT. The Two-Stage δ GSA was implemented to assess the impact of parameter uncertainty and correlations on key pharmacokinetic (PK) endpoints, AUC, C_max, and T_max. The most influential parameters were identified for the subsequent individual estimation by using the ITS method. Six simulated scenarios were designed by combining different sampling schedules (rich vs. sparse) and virtual sub-populations (real-case, best-case, worst-case), each reflecting specific variability patterns. Three optimization algorithms (Nelder-Mead, Powell, BFGS) were compared. Estimation performance was evaluated using Average Fold Error (AFE), Absolute AFE (AAFE), and Percentage Estimation Error (PEE). The Two-Stage δ GSA successfully identified the volume of distribution, clearance, and gastric emptying rate constant as the most influential parameters. Overall, estimation performance of the individual PK parameters and PK endpoints was provided. Most estimations yielded AFE and AAFE values between 0.8 and 1.25. Nelder-Mead showed the highest accuracy and precision. Both sampling strategy and individual variability impacted estimation quality. This work demonstrates the feasibility and value of combining correlation-aware GSA with individual parameter estimation in a semi-mechanistic PBPK framework. The integration of the Two-Stage δ GSA into PhysPK represents a major extension of the platform capabilities, providing a powerful tool to guide model simplification through dimensionality reduction of parameter space and support individual parameter estimation, especially under data-constrained conditions.