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Multifractal Analysis on Cancer Risk

  • Milan Stehlík
  • Philipp Hermann
  • Stefan Giebel
  • Jens-Peter Schenk
Chapter
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Here we consider retroperitoneal tumors in childhood as examples from oncology generating difficult multicriterial decision problems. Inter-patient heterogeneity causes multifractal behavior of images for mammary cancer. Here we fit mixture models to box-counting fractal dimensions in order to better understand this variability. In this context the effect of chemotherapy is studied. The approach of Shape Analysis, proposed already in the work of Giebel (Bull Soc Sci Med Grand Duche Luxemb 1:121–130, 2008; Zur Anwendung der Formanalyse. Application of shape analysis. University of Luxembourg, Luxembourg, 2011), is used. This approach has considered a small number of cases and the test according to Ziezold (Biom J 3:491–510, 1994) is distribution free. Our method here is parametric.

Notes

Acknowledgements

Milan Stehlík acknowledges FONDECYT Regular No1151441 and LIT-2016-1-SEE-023 mODEC. This work was also supported by the Slovak Research and Development Agency under the contract No. SK-AT-2015-0019. Philipp Hermann was supported by ANR project DESIRE FWF I 833-N18.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Milan Stehlík
    • 1
    • 2
  • Philipp Hermann
    • 3
  • Stefan Giebel
    • 3
  • Jens-Peter Schenk
    • 4
  1. 1.Linz Institute of Technology (LIT) and Department of Applied StatisticsJohannes Kepler UniversityLinzAustria
  2. 2.Institute of StatisticsUniversidad de ValparaísoValparaísoChile
  3. 3.Department of Applied StatisticsJohannes Kepler UniversityLinzAustria
  4. 4.Division of Pediatric RadiologyUniversity Hospital of HeidelbergHeidelbergGermany

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