Applying a Global Sensitivity Analysis Workflow to Improve the Computational Efficiencies in Physiologically-Based Pharmacokinetic Modeling

Abstract

Traditionally, the solution to reduce parameter dimensionality in a physiologically-based pharmacokinetic (PBPK) model is through expert judgment. However, this approach may lead to bias in parameter estimates and model predictions if important parameters are fixed at uncertain or inappropriate values. The purpose of this study was to explore the application of global sensitivity analysis (GSA) to ascertain which parameters in the PBPK model are non-influential, and therefore can be assigned fixed values in Bayesian parameter estimation with minimal bias. We compared the elementary effect-based Morris method and three variance-based Sobol indices in their ability to distinguish “influential” parameters to be estimated and “non-influential” parameters to be fixed. We illustrated this approach using a published human PBPK model for acetaminophen (APAP) and its two primary metabolites APAP-glucuronide and APAP-sulfate. We first applied GSA to the original published model, comparing Bayesian model calibration results using all the 21 originally calibrated model parameters (OMP, determined by “expert judgment”-based approach) vs. the subset of original influential parameters (OIP, determined by GSA from the OMP). We then applied GSA to all the PBPK parameters, including those fixed in the published model, comparing the model calibration results using this full set of 58 model parameters (FMP) vs. the full set influential parameters (FIP, determined by GSA from FMP). We also examined the impact of different cut-off points to distinguish the influential and non-influential parameters. We found that Sobol indices calculated by eFAST provided the best combination of reliability (consistency with other variance-based methods) and efficiency (lowest computational cost to achieve convergence) in identifying influential parameters. We identified several originally calibrated parameters that were not influential, and could be fixed to improve computational efficiency without discernable changes in prediction accuracy or precision. We further found six previously fixed parameters that were actually influential to the model predictions. Adding these additional influential parameters improved the model performance beyond that of the original publication while maintaining similar computational efficiency. We conclude that GSA provides an objective, transparent, and reproducible approach to improve the performance and computational efficiency of PBPK models.

Characterizing Dryland Ecosystems Using Remote Sensing and Dynamic Global Vegetation Modeling

“…This is in accordance with Pareto's principle in which a model includes a few influential parameters, and a majority of non-influential parameters (Pappas et al, 2013). Multiple studies show that results of the Morris SA can be trusted for calibration purposes (Hsieh et al, 2018;Janse et al, 2010;Tian et al, 2016). All four parameters indicated as influential are indeed used in the photosynthesis sub-model of EDv2.2 which is directly related to GPP.…”

Well-tempered MCMC simulations for population pharmacokinetic models

“…TI allowed us to perform what is in essence a rather powerful posterior sensitivity analysis (Gelman et al 1996) for which detection of multi-modality was a prerequisite. Alternatives such as prior-based sensitivity analysis are definitely useful (Hsieh et al 2018;Melillo et al 2019), but it does not make full use of the data. Note also that the detection of the over-parameterization was partly enabled by the hierarchical structure of the population model with the intra-individual variance revealing signs of over-fitting.…”

“…Within each study, the individual subjects' data were averaged. The same data were used in Hsieh et al (2018).…”

“…The hierarchy consisted of studies as "individuals", with an overall average level above. The same framework was used by Hsieh et al (2018) in their sensitivity analysis of the model. Hsieh et al determined that only 15 of the original 21 parameters calibrated by Zurlinden and Reisfeld were really influential, and found another five other influential parameters worth calibrating.…”

“…The development of powerful numerical Markov chain Monte Carlo (MCMC) algorithms (Girolami and Calderhead 2011;Robert and Casella 2011) has fueled the increasing use of Bayesian methods. However, those algorithms are still very computationally intensive and for complex models or large datasets can take hours or days to reach convergence on current computers (Hsieh et al 2018). The problem is compounded by the fact that, in most cases, convergence should be assessed by running multiple simulated Markov chains (Gelman and Rubin 1992).…”