Comparison of Sensitivity Analysis Methods in the Context of a QSP Model for Gout
Authors: Dela An , Kenz Zackary 
Published: February 2025

Objectives: As quantitative systems pharmacology (QSP) models are increasingly used to inform key questions related to drug development, there is need for sensitivity analysis (SA) to inform an understanding of influential model parameters which can improve confidence in predictions [1,2]. Applying SA methods during QSP model development can be difficult due to model size, number of parameters, and nonlinearities. We compare three SA techniques to shed more light on the most influential parameters impacting a model output of interest. By applying these methods to a validated model with known responses, we aim to provide insight for when SA methods are applied to other QSP models. Methods: GOUTsym™ is composed of 25 ODEs and 39 algebraics representing pathways and processes important in representing plasma uric acid (UA) levels, including hepatic production, renal clearance pathways and gut contributions, and an embedded exposure model. A retrospective SA was conducted to improve the understanding of how 14 varied parameters influence simulated plasma UA. The SA methods compared were partial rank correlation coefficients (PRCC) [3-5], derivative-based analysis via singular value decomposition followed by QR factorization (SA-QR) of the sensitivity matrix [6-7], and variance-based Sobol’ method [8-9], which are suitable for nonlinear and complex models (as compared to local one-at-a-time methods). Results: The SA methods consistently identified 7-8 of the 14 total parameters as most influential. While the parameter ranking order for PRCC and SA-QR was nearly identical, the Sobol' ranking was different but still agreed on the 7 most influential parameters with the other two methods. PRCC and SA-QR methods incorporated a clear cut-off mechanism via a test of statistical significance and matrix numerical rank, respectively, which distinguish influential and non-influential parameters. The Sobol’ method required user interpretation for determining a threshold. Computational times differed significantly from minutes (PRCC) to hours (SA-QR) to days (Sobol’). A framework applying SA methods simplest to most complex in QSP models is potentially reasonable, based on this case study.Conclusions: Through this case study, we noted that less complex SA methods like PRCC and SA-QR have similar overall rankings to the Sobol’ method even in a complex QSP model. Sobol’ method requires fewer assumptions to implement but may be infeasible without significant computational resources. Each increase in complexity, from correlation-based to derivative-based to variance-based, provides a tradeoff between computation time versus more flexibility and capability to capture complex model responses. Further investigations could inform generalizability of this case study, but the results herein can help inform the choice of SA method during QSP model development.Citations: References: 1. Sher. Bull Math Biol. (2022): 84(3): 39.2. Braakman. CPT: PSP. (2022): 11(3): 264-289.3. Marino. J. Theor Biol. 254.1 (2008): 178-196.4. Pearson. Phil Trans Royal Soc London. 186 (1895): 343-414.5. Stigler. Stat Sci. (1989): 73-79.6. Olufsen and Ottesen. J Math Bio. 67.1 (2013): 39-68.7. Gallaher. Cancer Res. (2018): 2127-2139.8. Gortmaker. NE J Med. 329.14 (1993): 1008-1012.9. Saltelli. Technomet. 41.1 (1999): 39-56.