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Deep learning prediction of patient response time course from early data via neural-pharmacokinetic/pharmacodynamic modelling

Nature Machine Intelligence volume 3, pages 696–704 (2021)Cite this article

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Abstract

Longitudinal analyses of patient response time courses following doses of therapeutics are currently performed using pharmacokinetic/pharmacodynamic (PK/PD) methodologies, which require considerable human experience and expertise in the modelling of dynamical systems. By utilizing recent advancements in deep learning, we show that the governing differential equations can be learned directly from longitudinal patient data. In particular, we propose a novel neural-PK/PD framework that combines key pharmacological principles with neural ordinary differential equations. We applied it to an analysis of drug concentration and platelet response from a clinical dataset consisting of over 600 patients. We show that the neural-PK/PD model improves on a state-of-the-art model with respect to metrics for temporal prediction. Furthermore, by incorporating key PK/PD concepts into its architecture, the model can generalize and enable the simulations of patient responses to untested dosing regimens. These results demonstrate the potential of neural-PK/PD for automated predictive analytics of patient response time course.

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Fig. 1: Schematic diagram of the neural-PK/PD model.
Fig. 2: An llustration of the ability of neural-PK model to predict complete PK profiles from having being shown only the early PK data from the first dosing cycle.
Fig. 3: Comparisons of platelet predictions from pop-PK/PD model versus neural-PK/PD model in selected patients from the test set, whereby only data from t < 21 days is observed.
Fig. 4: Comparisons of the model prediction versus ground truth using the pop-PK/PD and neural-PK/PD models.
Fig. 5: Neural-PK/PD performing population simulations using n = 532 training patients.

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Data availability

Source data are provided with this paper. Additional data that support the findings of this study are available from the corresponding author on reasonable request with the approval of Genentech. The raw data that underlies the findings of this study are not publicly available due to reasonable patient privacy concerns.

Code availability

The Wolfram Mathematica code for the neural-PK/PD model is available as Supplementary Software. It can be opened with the Wolfram Player Version 12.1.0 and above, which is freely downloadable from the link https://www.wolfram.com/player/.

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Acknowledgements

We would like to thank D. Lu, L. Brooks, G. Liu, K. Liu, K. Deng and A. Joshi for their discussions and helping to make this work possible.

Author information

Authors and Affiliations

  1. Department of Clinical Pharmacology, Genentech, South San Francisco, CA, USA

    James Lu, Brendan Bender & Jin Y. Jin

  2. Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI, USA

    Yuanfang Guan

Authors
  1. James Lu
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  2. Brendan Bender
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Contributions

J.L. conceived the study. J.L. and J.Y.J. designed the study. J.L., B.B., J.Y.J. and Y.G. performed data analysis. J.L., B.B., J.Y.J. and Y.G. wrote the manuscript.

Corresponding authors

Correspondence to James Lu or Jin Y. Jin.

Ethics declarations

Competing interests

J.L., B.B., J.Y.J. are employees of Genentech and own stock in Roche. The work was performed when Y.G. served as a consultant to Genentech. The remaining authors declare no competing interests.

Additional information

Peer review information Nature Machine Intelligence thanks Jorrit Enserink, Jing Tang and Giovanni Di Veroli for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Supplementary Figure 1.

a, The neural-PK schematic diagram. b, Detailed views into the ‘PKODE’ sub-module, which shows an implementation of the forward Euler step that explicitly incorporates the dosing data via the network port ‘Dose’. The network shown in (b) is a recurrent network, which unfolds in time whereby successive ‘NewPKState’ is fed into ‘PrevPK’. The ‘Δt*’ is a layer that multiplies the output of ‘PKVF’ by the constant step size ∆t. The numbers in grey denote the dimension of the arrays involved in the computational graph.

Supplementary information

Reporting Summary

Supplementary Software

A ZIP file containing a README, and a Mathematica notebook containing model code.

Source data

Source Data Fig. 2

Pharmacokinetic data versus time.

Source Data Fig. 3

Pharmacodynamic (platelet) data versus time.

Source Data Fig. 4

Predicted platelet count from pop-PK/PD and neural-PK/PD models versus data.

Source Data Fig. 5

Platelet count data for Q3W patients.

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Lu, J., Bender, B., Jin, J.Y. et al. Deep learning prediction of patient response time course from early data via neural-pharmacokinetic/pharmacodynamic modelling. Nat Mach Intell 3, 696–704 (2021). https://doi.org/10.1038/s42256-021-00357-4

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