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A mathematical model for the quantification of a patient’s sensitivity to checkpoint inhibitors and long-term tumour burden

Abstract

A large proportion of patients with cancer are unresponsive to treatment with immune checkpoint blockade and other immunotherapies. Here, we report a mathematical model of the time course of tumour responses to immune checkpoint inhibitors. The model takes into account intrinsic tumour growth rates, the rates of immune activation and of tumour–immune cell interactions, and the efficacy of immune-mediated tumour killing. For 124 patients, four cancer types and two immunotherapy agents, the model reliably described the immune responses and final tumour burden across all different cancers and drug combinations examined. In validation cohorts from four clinical trials of checkpoint inhibitors (with a total of 177 patients), the model accurately stratified the patients according to reduced or increased long-term tumour burden. We also provide model-derived quantitative measures of treatment sensitivity for specific drug–cancer combinations. The model can be used to predict responses to therapy and to quantify specific drug–cancer sensitivities in individual patients.

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Fig. 1: Example model fits to clinical immunotherapy response.
Fig. 2: Distribution of model parameters against immune response.
Fig. 3: Patient response classification by ROC analysis.
Fig. 4: Correlation analysis of the literature-derived calibration cohort revealed significant correlation between measured values and model-predicted variables.
Fig. 5: Immune response strength is associated with predicted and measured long-term tumour burden.

Data availability

All of the data supporting the results in this study are available within the paper and its Supplementary Information. The raw, de-identified patient data are available from the corresponding authors upon reasonable request and subject to Institutional Review Board approval.

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Acknowledgements

The research reported in this manuscript was supported by the National Science Foundation grant DMS-1930583 (to Z.W. and V.C.), National Institutes of Health grants 1U01CA196403 (to Z.W., E.J.K. and V.C.), 1U01CA213759 (to Z.W. and V.C.), 1R01CA226537 (to Z.W. and V.C.), 1R01CA222007 (to Z.W., G.A.C. and V.C.) and U54CA210181 (to Z.W., E.J.K. and V.C.) and the University of Texas System STARs Award (to V.C.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Authors

Contributions

J.D.B. implemented the model and collected the data. Z.W. and V.C. initiated the project, participated in data collection and supervised the model development and analysis. J.D.B., Z.W., M.P., P.D. and V.C. performed the model analysis. D.E., K.A.A.F., G.V.M., C.C., E.J.K., J.W.W. and D.S.H. participated in data collection. J.D.B., Z.W., D.E., K.A.A.F., M.P., G.A.C., P.D., S.N., J.R.-R., G.V.M., H.A.T., C.C., E.J.K., J.W.W., D.S.H. and V.C. interpreted the data and model results. J.D.B., Z.W., M.P., E.J.K. and V.C. wrote the manuscript.

Corresponding authors

Correspondence to Zhihui Wang or Vittorio Cristini.

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Competing interests

J.W.W. reports research support from GlaxoSmithKline, Bristol Myers Squibb, Merck, Nanobiotix, Mavupharma and Checkmate Pharmaceuticals. J.W.W. serves on the scientific advisory board for RefleXion Medical, MolecularMatch, OncoResponse, Checkmate, Mavupharmaceuticals and Alpine Immune Sciences. J.W.W. is co-founder of Healios Oncology, MolecularMatch and OncoResponse and serves as an advisor to AstraZeneca, Merck, MolecularMatch, Incyte, Aileron and Nanobiotix. J.W.W. has the following patents: MP470 (amuvatinib), MRX34 regulation of PD-L1, and the X-ray tomography technique to overcome immune resistance. The University of Texas MD Anderson Cancer Center has a trademark for RadScopal.

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Supplementary Methods, Discussion, Figs. 1–10, Tables 1–5 and references.

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Butner, J.D., Wang, Z., Elganainy, D. et al. A mathematical model for the quantification of a patient’s sensitivity to checkpoint inhibitors and long-term tumour burden. Nat Biomed Eng (2021). https://doi.org/10.1038/s41551-020-00662-0

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