Dominic Stefan Braem (1), Bernhard Steiert (2), Britta Steffens (1), Marc Pfister (1), and Gilbert Koch (1)
(1) Pediatric Pharmacology and Pharmacometric, University Children’s Hospital Basel, Switzerland (2) Roche Pharma Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, F. Hoffmann-La Roche Ltd., Basel, Switzerland
Objectives: Neural ordinary differential equations (NODEs) are a machine learning approach to model dynamic data [1]. Compared to commonly applied ODEs, the right-hand side of NODEs is not described with explicit, mechanism-based functions but consists of neural networks (NNs). This has the advantage that the correct structural model can be learned from the data instead of being defined by the modeler. In the past few years, NODEs have gained increasing attention in pharmacometrics (PMX) [2, 3, 4]. Different approaches for NODEs, such as encoder-decoder structures [2] or low-dimensional NODEs [4], were already applied to PMX data and have shown their potential to model such data. However, applications of NODEs were implemented in specialized software packages, such as Python or Julia, not including inter-individual variability. The aim of this work is to present the implementation of NODEs with inter-individual variability in common PMX software packages, such as Monolix, NONMEM, and nlmixr.
Methods: NODE structures consist of large, multi-dimensional NNs with multiple layers, resulting in a much higher number of parameters to estimate compared to mechanism-based models in PMX. Consequently, fitting such large NODEs in common PMX software packages cannot be done efficiently. Thus, the concept of low-dimensional NODEs [4] was leveraged to decrease the size of NODEs, and consequently decrease the number of model parameters to a level that common PMX software can handle. Such NODEs were coded in the model language of Monolix, NONMEM, and nlmixr. Further, inter-individual variability was introduced on model parameters in NODEs. Software-specific workflows that provides robust and reliable NODE fits were developed. In addition, scientific machine learning approaches [3], i.e., mechanism-based modelling was utilized for known model parts and NNs were utilized for unknown model parts, were applied. The presented NODE approach was tested on several example datasets provided in the Monolix library, including typical pharmacokinetic (PK) data (oral and intravenous drug administration, multiple dosing, parent-metabolite observations, and target-mediated drug disposition), pharmacodynamic (PD) data (indirect response), and survival data.
Results: NODE approachs developed in Monolix, NONMEM, and nlmxir was capable of fitting well all data, including PK, PD, survival, and count data. Population fits as well as individual fits were comparable with classical, mechanism-based modelling regarding structural description of the data and predictivity after an EBE step. Due to structural features of NODEs, VPCs are not applicable. However, inter-individual variability could be visualized in simulation plots where parameters were sampled from the conditional parameter distributions instead of the entire parameter distributions.
Conclusions: Implementation of NODEs in common PMX software packages opens the door of applying NODEs to facilitate PK, PD, and survival analysis for a broad PMX community without the need of learning additional programming languages, such as Python and Julia.
References:
[1] Chen RTQ, Rubanova Y, Bettencourt J, Duvenaud D (2018) Neural ordinary differential equations. arXiv: 1806.07366. https://doi.org/10.48550/arXiv.1806.07366
[2] 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:. https://doi.org/10.1016/j.isci.2021.102804
[3] Rackauckas C, Ma Y, Martensen J et al. (2021) Universal Differential Equations for Scientific Machine Learning. arXiv: 2001.04385. https://doi.org/10.48550/arXiv.2001.04385
[4] Bräm D, Nahum U, Schropp J et al. (2023) Low-dimensional neural ODEs and their application in pharmacokinetics. J Pharmacokinet Pharmacodyn: https://doi.org/10.1007/s10928-023-09886-4
Reference: PAGE 32 (2024) Abstr 10870 [www.page-meeting.org/?abstract=10870]
Poster: Methodology – AI/Machine Learning