Evaluation of the utility and efficiency of MATLAB and R-based packages for the development of quantitative systems pharmacology models
Victor Sokolov (1), Artem Dolgun (1), Veronika Voronova (1), Tatiana Yakovleva (1), Henning Schmidt (2), Nidal Al-Hunity (3), Gabriel Helmlinger (3), Kirill Peskov (1)
(1) M&S Decisions, Moscow; (2) IntiQuan, Switzerland; (3) Quantitative Clinical Pharmacology, IMED Biotech Unit, AstraZeneca, Waltham, MA, USA
Objectives: Quantitative systems pharmacology (QSP) modeling is an integrative methodology used in support of drug efficacy and safety problems in pharmaceutical R&D [1]. The growing need for QSP modeling in the industry and in communications with regulators necessitates a more standardized, transparent and seamless workflow within a model development and testing environment [2]. We selected five packages designed in MATLAB and R, to evaluate their utility and efficiency through comparison of the corresponding workflows, which were tested across three semi-mechanistic QSP models.
Methods: We evaluated the performance and model development capabilities of five packages: the MATLAB-based IQM toolbox [3], mrgsolve [4], RxODE [5], the AZR ODE solver with a set of MSDr functions [6], and the IQR package [7], all five packages running in R. Each package was tested over three different QSP models: a model describing lipoprotein metabolism and PCSK9-targeting therapies (PCSK9 model: 17 ODEs, 47 parameters) [8], a model of renal glucose reabsorption (SGLT model: 23 ODEs, 45 parameters) [9], and a GLP1-stimulated food retention model (FR model: 11 ODEs, 25 parameters) [10]. All three models were developed using study-level data, with substantial mechanistic details and non-linear features. The QSP modeling workflow was executed step-by-step, for each package and each model, testing solver speed (for numerical solution of the ODE system), quality of visualization, parameter estimation algorithms, model diagnostic options, and compatibility with companion workflows of pharmacometrics.
Results: The IQM, AZR/MSDr and IQR use a highly flexible syntax, and handle standardized ‘.csv’ datasets as inputs, thereby allowing the user to translate models and data from one package to another with minimal efforts, and regardless of the software environment (R or MATLAB). These modeling tools feature integrated parameter estimation tools, use a script-based workflow complemented with a user-friendly graphical user interface (GUI), and provide easy reproducibility and access to data exploration, parameter estimation and model simulation tasks.
RxODE and mrgsolve have proven to be powerful tools for simulations of population and QSP models with varying degrees of complexity and design. For both of these packages, the model structure is described in R code, and both packages may receive input from standardized datasets. mrgsolve is compatible with parameter estimation packages such as nlme, and nlmixr is used as the parameter estimation tool for RxODE-based simulations.
Solving of an ODE system with 20,000 time steps, for a single administration of a drug, was successfully performed in IQM, AZR/MSDr, IQR, mrgsolve and RxODE using the three QSP models. The RxODE was more than 10 times faster, in terms of solver speed, as compared to the other four. However, lag times could not be incorporated in RxODE-type models, and only mrgsolve and IQR were able to incorporate regression parameters from the datasets.
A parameter estimation procedure was carried out for 10, 5 and 7 parameters, based on study-level datasets with 876, 304 and 190 data points for the PCSK9, SGLT and FR models in IQM, IQR, AZR/MSDr and RxODE (nlmixr). AZR/MSDr, RxODE and IQM single-subject fitting was not stable compared to IQR. In addition to parameter estimation, the IQR package calculated the gradient and the Hessian of the objective function, providing 95% CI for fitted parameters and making the procedure very fast.
IQM, AZR/MSDr and IQR automatically provide common model diagnostics, e.g., Observed vs. Predicted, Residuals and Time profiles plots. In addition, AZR/MSDr and IQM provide sensitivity analyses, with a host of graphical features for longitudinal data or tornado plots for single timepoint.
Conclusion: We compared QSP workflows in IQM, AZR/MSDr, IQR, mrgsolve and RxODE packages using three QSP models. All packages can handle identical model structures and dataset files, as well as a script-based workflow. While the RxODE ODE solver was the fastest among five packages. IQR and mrgsolve are the only two packages which can operate with regression parameters, and IQR is the only package to provide a parameter estimation tool that is fast and robust, with an estimation of parameters with 95% CI. The IQM, AZR/MSDr and IQR packages provide rich model testing toolkits and various goodness-of-fit metrics for QSP modeling, with AZR/MSDr having superior quality of visual outputs.
References:
[1] Helmlinger G, et al. Eur J Pharm Sci. 2017 Nov 15;109S:S39-S46. doi: 10.1016/j.ejps.2017.05.028.
[2] Gadkar K, et al. CPT Pharmacometrics Syst Pharmacol. 2016 May;5(5):235-49. doi: 10.1002/psp4.12071.
[3] Sunnåker M, et al. ACoP7, 2016. http://www.intiquan.com/iqm-tools.
[4] Wang W, et al. CPT Pharmacometrics Syst Pharmacol. 2016 Jan;5(1):3-10. doi: 10.1002/psp4.12052.
[5] Baron K, et al., 2017. https://mrgsolve.github.io/
[6] Fox R, et al. ACoP8, 2017.
[7] http://www.intiquan.com/iqr-tools/
[8] Sokolov V, et al. ACoP8, 2017.
[9] Yakovleva T, et al. ACoP8, 2017.
[10] Voronova V, et al., PAGE, 2017.