Benefits of integrating machine learning with clinical pharmacology principles for predictive pharmacokinetic modeling
Diego Valderrama (1,2), Ana Victoria Ponce-Bobadilla (3), Sven Mensing (3), Holger Fröhlich (1,2), Sven Stodtmann (3)
(1) Department of Bioinformatics, Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany (2) Bonn-Aachen International Center for Information Technology (B-IT), University of Bonn, Bonn, Germany (3) AbbVie Deutschland GmbH & Co. KG, Ludwigshafen, Germany
Introduction:
Machine learning (ML) applications in clinical pharmacology have been rapidly increasing over the last several years (1). While most current approaches use ML techniques as black boxes, few works have proposed interpretable architectures which integrate mechanistic knowledge (2,3). Following this line of research, we considered a one-compartment PK model using a Scientific Machine Learning (SciML) framework that learns an atypical absorption process using neural networks, while simultaneously estimating classical parameters of drug distribution and elimination. We compared the performance of this framework against two other proposed architectures (4,5) at typical extrapolation tasks that occur in drug development programs.
Methods:
PK data of 800 subjects were simulated from a NLME model. This model consisted of a one-compartment model with Weibull-type absorption, linear clearance and small interindividual variability on clearance. A weekly subcutaneous dosing was assumed. Subjects were allocated into 8 dose groups: 80 mg, 100 mg, 120 mg, 140 mg, 160 mg, 180 mg, 200 mg and 220 mg. The PK profiles of these subjects were simulated for 70 days and recorded every 12 hours.
Different numbers of training subjects (48, 96, 280 and 680 subjects), sampling strategies of the training dataset (dense/sparse) and error models (additive/proportional) were considered to assess how these factors affect the predicting performance of the architectures and move toward more realistic datasets.
A PK-SciML architecture was implemented that consisted of an ODE describing the depot and the central compartment dynamics with a linear clearance term and a neural network term to capture the absorption rate. The neural network consists of two fully connected layers with a tanh activation function in between and a SoftPlus activation function at the end. The first layer takes the current value of the Depot compartment and the time since last dose as inputs and has 50 hidden neurons as output. The second layer contains a single output which represents the absorption rate.
We implemented two other architectures (4,5). We modified the architecture introduced by Bram et. al. (5) to allow the architecture to predict new patients.
The predictive performance of the architectures was analyzed for the training subjects and for 120 test subjects under the following scenarios: extrapolation beyond the time horizon of the training data, missing dose, complete cessation of dosing and extrapolation to different dose amounts (150 mg EW, 230 mg EW). The performance of the architectures was evaluated using evaluation metrics (MAPE, RSME), goodness-of-fit plots, residual plots and mean concentration-time profiles.
Results:
When considering the largest number of training subjects (680 patients), an additive error and dense PK sampling for the training data, all architectures showed high accuracy in the extrapolation test scenario for training subjects (0.9 ≤ RMSE ≤ 2.2, 3.1 ≤ MAPE ≤ 7.8 for all models). Only the PK-SciML architecture performed well in the dose cessation scenario (RMSE=0.9, MAPE=15.9) compared to 4.3 ≤ RMSE ≤ 5.7, 113.7≤ MAPE ≤ 175.3, for the other architectures.
As the number of training subjects decreased, PK-SciML outperforms the compared models in all tested scenarios. In a realistic dataset, the least training subjects (48), less intense sampling and proportional error, predictions by (4,5) were generally inaccurate (2.6 ≤ RMSE ≤ 18.5, 14.8 ≤ MAPE ≤ 366.9). In contrast, the PK-SciML architecture generated even in this case accurate predictions for all tasks (1.7 ≤ RMSE ≤ 4, 8.9 ≤ MAPE ≤ 13.8).
For all the tested scenarios, PK sampling schemes and different number of training subjects, PK-SciML predicts apparent clearance (CL) and apparent central volume (V) values which are closed to their original values used for generating the data.
Conclusions:
The proposed PK-SciML model learns an unknown absorption mechanism and PK relevant parameters simultaneously. This framework can be used for realistically sized datasets to accurately perform typical tasks during drug development: extrapolation to new doses.
We demonstrate that including known physiological structure into a SciML model allows us to obtain highly accurate predictions and preserving the interpretability of classical compartmental models.
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] 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. [3] 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. [4] 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. [5] 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. Disclosures:
A.V.P.B., SM and S.S. are employees of AbbVie and may hold AbbVie stock. Fraunhofer SCAI (employees: D.V., H.F.) received funding from AbbVie for this study. This study was sponsored by AbbVie and AbbVie contributed to the study design, research, and interpretation of data, and the writing, reviewing, and approving of the publication.