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A tutorial review of mathematical techniques for quantifying tumor heterogeneity

1 Department of Mathematics and Statistics, Haverford College, Haverford, PA, USA
2 Department of Mathematics, North Carolina State University, Raleigh, NC, USA
3 Department of Medical Imaging, University of Arizona, Tucson, AZ, USA
4 Department of Mathematics, Humboldt State University, Arcata, CA, USA
5 Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA
6 Statistical and Applied Mathematical Sciences Institute, Durham, NC, USA
7 Department of Molecular Biomedical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, NC, USA
8 Department of Materials Design and Innovation, University at Buffalo, Buffalo, NY, USA
9 Department of Applied Mathematics, University of California, Merced, Merced, CA, USA

Special Issues: Mathematical modeling of tumor heterogeneity

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018–2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.
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