Linda Wanika1, Ine Skottheim Rusten2, James Kermode1, Mike Chappell1
1University of Warwick, 2Systems Resource Lab
Introduction: The ecosystem for the rapid adoption of simulation methods (ERAMET) EU project aims to create a credibility framework for orphan and paediatric drug development modelling and simulation. Uncertainty quantification (UQ) is a key aspect in modelling and simulation as it provides a summary of the parameter distribution(s) used to derive the fixed and random effects of the model. However, the application of UQ to mixed effects (ME) models remains a challenge as numerical issues can arise with the estimation of relative standard errors (RSEs). Moreover, structural, and practical identifiability of the model with respect to the data additionally remain a challenge. A lack of UQ in ME modelling could result in the generation of an unreliable model. To highlight techniques to overcome these challenges, an exemplar use case with a one compartment PK model was developed to characterise the PK of warfarin in adults. This use case highlights the range of UQ applicability from the structure of the model to an assessment of whether an ordinary differential equation (ODE) model structure is sufficient to fit to the available data. Aims: • Outline and assess UQ techniques that may be required for credible model development using a one ME compartment model for warfarin PK. Methods: Plasma concentration profiles for fifty individuals who were administered 100mg of warfarin were extracted from [1]. The ME modelling was based on a one compartment model, where the parameters estimated are the absorption rate, KA, clearance, CL, and volume of distribution, VD. Below is a summary of some of the UQ techniques that were performed prior to parameter estimation: • Software quality assurance: All R packages in the CRAN repository have been reviewed and verified • ODE solver: All ODE solvers that can be used are documented with specific ODE solver settings • Structural identifiability analysis: Model and unknown model parameters are structurally identifiable • Sensitivity analysis: Analysis was conducted, and the model simulation aligned with the warfarin plasma profile • Practical identifiability analysis: Model and parameters are practically identifiable ME modelling was performed in STAN using a Hamiltonian Monte Carlo approach. Probability distributions were evaluated for alternative UQ measurements. A sum of two exponents function was fitted and compared to the ODE model to assess its appropriateness. Results: The overall likelihoods for the one compartment model and the sum of two exponents function were -716 and -1072, respectively. The one compartment model has a higher likelihood of characterising the observed data compared to the sum of exponents function. The population parameter estimates for the one compartment model and additional UQ measures are provided below: • KA (hr-1) Mean: Estimate: 0.307, 95% CDI LB: 0.336, 95% CDI UB: 0.400, 95% CDI Ratio AVRG: 0.916 • CL (L/hr) Mean: Estimate: 1.014, 95% CDI LB: 0.979, 95% CDI UB: 1.050, 95% CDI Ratio AVRG: 0.965 • VD (L) Mean: Estimate: 8.177, 95% CDI LB: 7.636, 95% CDI UB: 8.722, 95% CDI Ratio AVRG: 0.936 • KA (hr-1) Standard Deviation: Estimate: 0.199, 95% CDI LB: 0.158, 95% CDI UB: 0.241, 95% CDI Ratio AVRG: 0.810 • CL (L/hr) Standard Deviation: Estimate: 0.405, 95% CDI LB: 0.357, 95% CDI UB: 0.451, 95% CDI Ratio AVRG: 0.890 • VD (L) Standard Deviation: Estimate: 0.590, 95% CDI LB: 0.531, 95% CDI UB: 0.653, 95% CDI Ratio AVRG: 0.902 • a (fixed effects only) Error Model Constant: Estimate: 1.306, 95% CDI LB: 1.232, 95% CDI UB: 1.384, 95% CDI Ratio AVRG: 0.943 • a (ME) Error Model Constant: Estimate: 0.890, 95% CDI LB: 0.836, 95% CDI UB: 0.953, 95% CDI Ratio AVRG: 0.937 95%CDI: 95% credible interval, LB: lower bound, UB: upper bound. AVRG: average. Note the 95% CDI average was computed by dividing the intervals by the parameter estimates and calculating the mean of these values. Conclusion: The approaches applied illustrate that this model and data are both structurally and practically identifiable with respect to the available data, offering confidence for future users in use of this model in this context. The 95% credible intervals enable users to observe the certainty surrounding the probability distributions and, as the ratios are >0.75, these distributions are implied to be narrow, indicating increased credibility of the parameter estimates, with respect to the data. Such UQ analysis can be implemented in future ME model development to enable users to assess the credibility of published models prior to implementation.
1. https://dataset.lixoft.com/data-set-examples/warfarin-data-set/ (note that the dataset in the Monolix demo consists of 50 patients)
Reference: PAGE 33 (2025) Abstr 11744 [www.page-meeting.org/?abstract=11744]
Poster: Methodology - Model Evaluation