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Prediction in Cancer Genomics Using Topological Signatures and Machine Learning

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Book cover Topological Data Analysis

Part of the book series: Abel Symposia ((ABEL,volume 15))

Abstract

Copy Number Aberrations, gains and losses of genomic regions, are a hallmark of cancer and can be experimentally detected using microarray comparative genomic hybridization (aCGH). In previous works, we developed a topology based method to analyze aCGH data whose output are regions of the genome where copy number is altered in patients with a predetermined cancer phenotype. We call this method Topological Analysis of array CGH (TAaCGH). Here we combine TAaCGH with machine learning techniques to build classifiers using copy number aberrations. We chose logistic regression on two different binary phenotypes related to breast cancer to illustrate this approach. The first case consists of patients with over-expression of the ERBB2 gene. Over-expression of ERBB2 is commonly regulated by a copy number gain in chromosome arm 17q. TAaCGH found the region 17q11-q22 associated with the phenotype and using logistic regression we reduced this region to 17q12-q21.31 correctly classifying 78% of the ERBB2 positive individuals (sensitivity) in a validation data set. We also analyzed over-expression in Estrogen Receptor (ER), a second phenotype commonly observed in breast cancer patients and found that the region 5p14.3-12 together with six full arms were associated with the phenotype. Our method identified 4p, 6p and 16q as the strongest predictors correctly classifying 76% of ER positives in our validation data set. However, for this set there was a significant increase in the false positive rate (specificity). We suggest that topological and machine learning methods can be combined for prediction of phenotypes using genetic data.

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Acknowledgements

JA was partially supported by NSF DMS 1854770 and NSF CCF 1934568. RS was partially supported by the Simons Collaboration Grant 318086 in the early stages of this project and NSF DMS 1854705.

Author information

Authors and Affiliations

  1. Department of Molecular and Cellular Biology, University of California, Davis, CA, USA

    Georgina Gonzalez

  2. Department of Statistics, University of California, Davis, CA, USA

    Arina Ushakova

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Radmila Sazdanovic

  4. Department of Molecular and Cellular Biology, and Department of Mathematics, University of California, Davis, CA, USA

    Javier Arsuaga

Authors
  1. Georgina Gonzalez
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  2. Arina Ushakova
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  3. Radmila Sazdanovic
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  4. Javier Arsuaga
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Corresponding author

Correspondence to Javier Arsuaga .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, NTNU, Trondheim, Norway

    Nils A. Baas

  2. Department of Mathematics, Stanford University, Stanford, CA, USA

    Gunnar E. Carlsson

  3. Department of Mathematical Sciences, NTNU, Trondheim, Norway

    Gereon Quick

  4. Department of Mathematical Sciences, NTNU, Trondheim, Norway

    Markus Szymik

  5. Department of Mathematical Sciences, NTNU, Trondheim, Norway

    Marius Thaule

Appendix

Appendix

See Tables 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.

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Gonzalez, G., Ushakova, A., Sazdanovic, R., Arsuaga, J. (2020). Prediction in Cancer Genomics Using Topological Signatures and Machine Learning. In: Baas, N., Carlsson, G., Quick, G., Szymik, M., Thaule, M. (eds) Topological Data Analysis. Abel Symposia, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-43408-3_10

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