Multifractal Analysis on Cancer Risk

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.