MaS: population pharmacometric modeling in Python
Chongyi Xu (1), Jiesen Yu (1), Wenjie Cao (1), Haikuo Lu (1), Ze Yao (1), Xin Sun (1), Kaifan Zhang (1), Jieren Luo (2), Qingshan Zheng (2), Han Zheng (1)
(1) Shanghai BioGuider Medical Technology Co., Ltd., China, (2) Shanghai University of Traditional Chinese Medicine, China
Introduction: MaS [1] is a software package for modeling and simulation in pharmacometrics and statistics. Its modeling language is built in Python, enabling seamless integration with popular machine-learning libraries such as PyTorch [2] and TensorFlow [3]. To optimize modeling efficiency, MaS employs closed-form ODEs for commonly used compartment models. The estimation methods, including FOCE-I and SAEM, are implemented in C++ for fast processing speeds. User-written models are programmed in Python, and automatically translated to C++ to ensure that users benefit from the easy language grammar in Python and the fast speed of C++. MaS also includes popular diagnostic tools such as graphical checking functionalities similar to xpose [4], as well as model diagnostics/covariate modeling-building methods such as VPC, bootstrap, and SCM.
Objectives: In this study, we examined the performance of the FOCE-I and SAEM estimation methods implemented in MaS compared to those in NONMEM [5] and nlmixr [6], and Monolix [7] and nlmixr, respectively.
Methods: To ensure comparability with Schoemaker et al.'s study [6], we carried out a simulation study with similar scenarios. Richly and sparsely sampled PK data were simulated for three dose levels (10, 20, and 40mg) and 30 subjects per administration route (oral, IV bolus, and IV infusion), from different underlying models (1- and 2- compartment models, with linear or Michaelis-Menten clearance.) with 30% inter-individual variabilities for each PK parameter and 20% residual variabilities. We simulated 1000 replicates for each scenario and compared the estimated values with the true values (the scenario setting) to assess the presence of bias. We also compared the empirical standard errors (the standard deviation of the estimates from the 1000 replicates) with the mean of the standard errors to evaluate the accuracy of the standard errors.
Results: Our simulation study found that the estimates of the population parameters, particularly theta and omega, were consistent across all software packages in most scenarios, with IIV estimates for Ka showing more variability. The estimates were generally close to the true values, and the corresponding estimated standard errors were close to the empirical standard errors.
Conclusion: The results of our simulation study demonstrate that MaS is a valuable tool for nonlinear mixed-effects modeling. Specifically, MaS provides a flexible and versatile modeling language that enables the representation and description of a wide range of model structures and study designs. Furthermore, its workflow is aligned with the PyTorch library, thereby streamlining the integration of machine learning models into traditional PK-PD workflows. This attribute is particularly noteworthy given the current trend towards the integration of machine learning approaches in various research areas, including pharmacokinetic and pharmacodynamic modeling [8][9]. With the fast progress in both areas, the hybrid approach has the potential to enhance our understanding of drug action, enable more accurate predictions of drug response, and ultimately improve patient outcomes.
References:
[1] https://www.drugchina.net/mas
[2] https://pytorch.org/
[3] https://www.tensorflow.org
[4] https://CRAN.R-project.org/package=xpose
[5] https://www.iconplc.com/innovation/nonmem/
[6] Schoemaker et al. (2019), ‘Performance of the SAEM and FOCEI Algorithms in the Open-Source, Nonlinear Mixed Effect Modeling Tool Nlmixr’.
[7] Laveille C et al PAGE 17 (2008) Abstr 1356 [www.page-meeting.org/?abstract=1356]
[8] Liu, X., Liu, C., Huang, R., Zhu, H., Liu, Q., Mitra, S., and Wang, Y. (2021). Long short-term memory recurrent neural network for pharmacokinetic pharmacodynamic modeling. Int. J. Clin. Pharmacol. Ther. 59, 138–146.
[9] Lu, J., Deng, K., Zhang, X., Liu, G., & Guan, Y. (2021). Neural-ODE for pharmacokinetics modeling and its advantage to alternative machine learning models in predicting new dosing regimens. Iscience, 24(7), 102804.