Diego Valderrama (1), Ana Victoria Ponce-Bobadilla (2), Sven Mensing (2), Holger Fröhlich (1,3), Sven Stodtmann (2)
(1) Department of Bioinformatics, Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany (2) AbbVie Deutschland GmbH & Co. KG, Ludwigshafen, Germany (3) Bonn-Aachen International Center for Information Technology (B-IT), University of Bonn, Bonn, Germany
Introduction:
The last few years have seen a remarkable rise in the use of machine learning (ML) in clinical pharmacology [1]. Even though most existing approaches deploy ML techniques as black boxes [2, 3], some studies have suggested interpretable architectures that incorporate mechanistic information [4-6]. In particular, [6] presented a Scientific Machine Learning (SciML) method for estimating relevant PK parameters and learning an unknown absorption process of a PK system through a neural network. While the model produced encouraging findings, it did not integrate inter-individual heterogeneity of the PK processes. We extended this framework and proposed a new method that estimates population parameters and their interindividual variability and also captures a complex absorption mechanism and the inter-individual variability (IIV) through a neural network term.
Methods
We simulated PK data using a two-compartment model with a mixed zero-and first-order absorption, linear clearance and interindividual variability on clearance, volume and absorption. Patients with different dose administration regimens with both sparse and intense pharmacokinetic sampling were simulated.
To evaluate the performance of our model, the PK data was split into 80% training and 20% test. We ensured that both splits included a similar fraction of patients with intensive and sparse sampling. The concentration-time profile prediction performance was evaluated using MAE and RMSE. For a graphical evaluation, goodness of fit plots (GOF), eta distribution plots and prediction-corrected visual predictive checks (pcVPCs) were created for both training and test sets.
Following [6], we proposed a REPK-SciML model where the depot, central, and peripheral compartment dynamics were described by an ODE with a linear clearance term and a neural network term to represent the absorption rate. The neural network consists of fully connected layers with SoftPlus activation functions and instance normalization. The last layer produces only one output which represents the absorption rate. The first layer takes as input the concatenation of the last dose, the current value of the Depot compartment, the time since the last dose and some absorption parameters (AbsPars) which can be thought of as other system parameters that are defined in the same way as parameters with IIV.
We employ an additional neural network to learn the IIV on Clearance, Volume and AbsPars. The neural network is a Time-LSTM [7] and takes as input the concentration, the cumulative sum of doses since the last concentration, and the time since the last dose. Furthermore, to complement our loss function, we propose to use a FOCE-based loss function to force the model to learn good eta distributions, following NONMEM principles.
Results
The GOF plots and individual plots show a good agreement between the simulated and the predicted concentration-time profiles. The good performance can also be observed in the performance metrics.
The predicted population parameters of apparent clearance (CL) and apparent central volume (V) approximate the values used to synthesize the data. The distribution of the individual parameters also shows good resemblance. Finally, the pcVPCs show that the model can describe well the variability.
Conclusion
The proposed REPK-SciML model addresses clinical data challenges such as having patients in different phases of clinical studies. We demonstrate that using a FOCE-based loss function the model learns IIV, population parameters as well as a complex absorption mechanism that allow us to accurately predict patient specific concentration-time profiles.
References:
[1] Janssen, A., Bennis, F. C. & Mathôt, R. A. A. (2022). Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations. Pharmaceutics, 14(9), 1814.
[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(7), 102804.
[3] Bräm, D. S., Parrott, N., Hutchinson, L. & Steiert, B. (2022). Introduction of an artificial neural network–based method for concentration-time predictions. CPT: Pharmacometrics & Systems Pharmacology, 11(6), 745–754.
[4] Janssen, A., Leebeek, F. W. G., Cnossen, M. H., … Keeling, D. (2022). Deep compartment models: A deep learning approach for the reliable prediction of time-series data in pharmacokinetic modeling. CPT: Pharmacometrics & Systems Pharmacology, 11(7), 934–945.
[5] Qian, Z., Zame, W., Fleuren, L., Elbers, P., & van der Schaar, M. (2021). Integrating expert ODEs into Neural ODEs: Pharmacology and disease progression. Advances in Neural Information Processing Systems, 34, 11364-11383.
[6] Valderrama, D., Ponce‐Bobadilla, A. V., Mensing, S., Fröhlich, H., & Stodtmann, S. (2024). Integrating machine learning with pharmacokinetic models: Benefits of scientific machine learning in adding neural networks components to existing PK models. CPT: Pharmacometrics & Systems Pharmacology, 13(1), 41-53.
[7] Baytas, I. M., Xiao, C., Zhang, X., Wang, F., Jain, A. K., & Zhou, J. (2017, August). Patient subtyping via time-aware LSTM networks. In Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining (pp. 65-74).
Reference: PAGE 32 (2024) Abstr 11015 [www.page-meeting.org/?abstract=11015]
Poster: Methodology – AI/Machine Learning