Thibaud Derippe (1,2,3), Sylvain Fouliard (1), Xavier Declèves (2), Donald E. Mager (3,4)
(1) Institut de Recherches Internationales Servier, Suresnes, France ; (2) Université de Paris, Inserm, UMRS-1144, Optimisation Thérapeutique en Neuropsychopharmacologie, F-75006 Paris, France ;(3) Department of Pharmaceutical Sciences, University at Buffalo, SUNY, USA ; (4) Enhanced Pharmacodynamics, LLC, Buffalo, NY, USA
Introduction/Objectives: The generation of Virtual Patients (VPs) is a common task in Quantitative System Pharmacology (QSP). In the most classical approach, VP parameter values are sampled within pre-defined physiological bounds, before using an ordinary differential equation (ODE) solver to compute outputs of interest (OoI). These OoI are identified states of the QSP model with a biological/clinical meaning and may correspond to the data used for model qualification. Because some computed OoI might be outside target ranges, it is often needed to add a data/simulation comparison step to accept only the physiological VPs and reject the others [1]. In some cases, the percentage of rejection can be so high that, coupled with the time-consumption of ODE-solving, finding a sufficient number of plausible VPs to constitute a population is a real struggle. Based on the principle that some parameters have a predictable impact on the OoI, an algorithm was developed to accelerate this VP acceptance/rejection step and ultimately the workflow.
Methods: A PK/PD tumor growth inhibition (TGI) model [2] (5 states; tumor size as OoI) was used to develop the methodology and analyze the technical performance of our algorithm, then the approach was extended to a QSP model of apoptosis [3] (65 states; apoptosis trigger as OoI). First, model parameters were categorized into four “monotonic” sets according to the partial derivative of OoI with the parameter (always positive, always negative, always null, or fluctuating), and cohorts of 200,000 potential VPs were manually generated. Then, two steps were iteratively repeated until all VPs were either accepted or rejected. First, 2,000 VPs were sampled among the cohort, and their OoI were computed through simulations and compared to pre-defined targets. Secondly, their outcomes were extrapolated to other VPs based on relative parameter values and the associated monotonic sets. For instance, in case of an unphysiological high tumor size, all VPs having all parameter values leading to an equal or greater tumor size were also rejected: all VPs having equal or lower drug efficacy (k2), and equal or greater growth rate constants (lambda0, lambda1) and PK parameters (ke and Vd), and equal death transit rate constant (k1). Overall, parameter spaces for automatic rejection or acceptance were iteratively produced, reducing the number of ODE-solving steps. The performance of this algorithm was further tested with variations on model complexity and for parameter sampling space.
Results: Analyzing 200,000 VPs from the TGI model for the plausibility of their OoI using the optimized algorithm took 5 to 46 seconds (median = 22s), depending both on the percentage of VP rejection and the number of varying parameters. Comparatively, the classical method took 55 seconds. This gain can be approximated by the absolute number of extrapolated VPs (from 34 to 98 % of the 200,000 VPs), multiplied by the time needed for ODE solving (around 0.35 sec for 2000 VPs), minus the time needed to perform the extrapolations (from 1 to 20 s). The time benefit of our algorithm decreased with the number of varying parameters (by simultaneous reducing the number of extrapolated VPs and increasing the extrapolation time, both p-value < 0.05), but increased with either low or high rejection percentages (by increasing number of extrapolations, p-value < 0.05). Applied on the QSP model with 6 varying parameters, 200,000 VPs were analyzed between 24 seconds to 4 minutes, compared to more than 12 minutes for the standard approach (around 7 sec for solving 2,000 VP ODE). This highlights that increasing the model numerical complexity increases the impact of solving less ODE systems. Of note, the algorithm also allows for composite acceptance criteria, such as different types of OoI (e.g., biomarker values, clinical response, safety readouts), several targets per OoI (e.g., tumor shrinkage assessed at several different time-points), and/or behavior of readouts associated with several administration protocols.
Conclusions: Building plausible VP populations can be challenging owing to non-physiological profiles. Our new methodology can accelerate the acceptance/rejection steps. Further investigation on the monotonic nature of the OoI/parameter relationship will be needed. This work has been wrapped into a generic R package (available on GitHub soon using RxODE as the ODE solver [4]), allowing ready use of this methodology on other QSP models.
References:
[1] Rieger TR, Allen RJ, Musante CJ. Modeling is data driven: Use it for successful virtual patient generation. CPT: Pharmacometrics & Systems Pharmacology 2021;10:393–4. https://doi.org/10.1002/psp4.12630.
[2] Simeoni M, Magni P, Cammia C, Nicolao GD, Croci V, Pesenti E, et al. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 2004;64:1094–101. https://doi.org/10.1158/0008-5472.CAN-03-2524.
[3] Lindner AU, Concannon CG, Boukes GJ, Cannon MD, Llambi F, Ryan D, et al. Systems analysis of BCL2 protein family interactions establishes a model to predict responses to chemotherapy. Cancer Res 2013;73:519–28. https://doi.org/10.1158/0008-5472.CAN-12-2269.
[4] Wang W, Hallow K, James D. A tutorial on RxODE: Simulating differential equation pharmacometric models in r. CPT Pharmacometrics Syst Pharmacol 2016;5:3–10. https://doi.org/10.1002/psp4.12052.
Reference: PAGE 30 (2022) Abstr 10167 [www.page-meeting.org/?abstract=10167]
Poster: Methodology - New Modelling Approaches