San Francisco Bay Area Statistical
Association
Meeting
Time: |
4:30 – 6:00 pm, January 26, 2017 (4:30-5:00 networking and light refreshment, 5:00-6:00
seminar) |
Location: |
Department of Statistics, Stanford University, Sequoia Hall
Room 200 campus-map.stanford.edu provides
interactive campus map, search for
ŇSequoia HallÓ to location the building. Please note parking is free on campus after 4pm. |
Speaker: |
Professor Milan Stehlik Department of Applied Statistics, Johannes Kepler
University in Linz, Austria Linz Institute of Technology (LIT), Johannes Kepler University in Linz, Austria Institute of Statistics, Universidad de Valpara
́őso, Valpara ́őso, Chile Email: Milan.Stehlik@jku.at |
Title: |
Multi-fractal and Multi-criteria aggregation for cancer risk
assessment |
Abstract:
There exists a big need for discrimination between mammary
cancer and mastopathy tissues (see Hermann et al.
(2015)). Non invasive techniques generally may produce
inverse problems, e.g. estimating a Hausdorff fractal
dimension from boundary of examined tissue (see Kiselak
et al. (2013)). We will discuss these issues in the context of our recent
results (see e.g. Filus, Filus
and Stehl ́ők (2009)).
During the talk we will discuss several issues which bring light into both fractal
based cancer modelling and more general stochastic
geometry models and their comparisons.
When we consider fractal based cancer diagnostic, many times a
statistical procedure to assess the fractal dimension is needed. We shall look
for some analytical tools for discrimination between cancer and healthy ranges
of fractal dimensions of tissues. Baish and Jain
(2000) discussed planar tissue preparations in mice which
has a remarkably consistent scaling exponents (fractal dimensions) for tumor
vasculature even among tumor lines that have quite different vascular densities
and growth characteristics. In Stehl ́ők et al. (2015) we provide extensive study of cancer risk
assessment on simulated and real data and fractal based cancer. Both non-random
and random carpets have been validated for modelling
of the cancer growth, and it was shown that only random carpets can be used. We constructed a statistical test, which is
able to distinguish between the two groups, masthopathy
and mammary cancer (see Stehl ́ők et al. (2012)).
The inter-patient variability of fractal dimension for mammary
cancer is high (see Stehl ́ők
et al. (2016)) and therefore multifractality is a
better concept (see Nicolis et al. (2016)). This is a
feasible and parsimous solution for a more delicate
problem of multi-objective aggregation of information. This touches bases for
general topological approach for aggregation Stehl
́ők (2016), which links to Sugeno
integral as a way to aggregation in bornological
spaces.
The algebraic and topologic properties of cancer growth are
available via appropriate set structures, e.g. bornology
(see Paseka, Solovyov, and Stehl ́ők (2015), Paseka, Solovyov, and Stehl ́ők (2016)). Such
structures can be very useful for defining fractal cancer hypothesis. Nephroblastoma (given by Wilms tumour) is the typical tumour of
the kidneys appearing in childhood, which does not satisfy fractal cancer
hypothesis. We illustrate on recent pre/post clinical study the effect on
chemotherapy to Euclidean volumes of such tumors (see Hermann et al. (2015)b.)
Author acknowledges support of FONDECYT Regular N 1151441.
References
Baish J.W. and
Jain R.K. (2000). Fractals and cancer. Cancer Research, 60, 3683-3688.
Filus J., Filus L. and Stehl
́ők M. (2009). Pseudoexponential modelling of cancer diagnostic testing.
Biometrie und Medizinische Informatik,
Greifswalder Seminarberichte
Heft 15, 41-54.
Kiselak, J., Pardasani,K. R., Adlakha,N. Agrawal, M. and Stehl ́ők, M. (2013) On some
probabilistic
aspects of
diffusion models for tissue growth, The Open Statistics and Probability Journal
Hermann, P.; Mrkvicka, T.; Mattfeldt, T., Minarova, M.; Helisova, K.; Nicolis, O.; Wartner, F.;
Stehl ́ők M., (2015) Fractal and stochastic geometry inference for
breast cancer: a case study with
random fractal models and Quermass-interaction processÓ Statistics in Medicine,34,
2636-2661
Hermann, P., Giebel, S.M., Schenk, J.-P., and Stehl ́ők, M. (2015). Dynamic Shape Analysis - before
and after chemotherapy. Proc. International Conference on Risk Analysis (ICRA6), 339-346.
Nicolis, O., Kiselak, J. Porro, F. and Stehl ́ők, M. Multi-fractal
cancer risk assessment, Stochastic
Analysis and Applications, DOI:
10.1080/07362994.2016.1238766
Paseka, J., Solovyov, S. A. and Stehl ́ők, M. (2015) ÓLattice-valued bornological
systemsÓ, Fuzzy Sets
and Systems, 259, 15,
68-88
Paseka, J., Solovyov, S. A. and Stehl ́ők, M. (2016), On a topological
universe of L-bornological
spaces, Soft Computing
20:2503-2512
Stehl ́ők M., Mrkvi˙cka T., Filus J. and Filus L. (2012),
Recent development on testing in cancer risk:
a fractal and stochastic
geometry, Journal of Reliability and Statistical Studies Vol. 5, 83-95.
Stehl ́ők,M., Giebel,
S. M., Prostakova,J. Schenk J.P. (2014), Statistical
inference on fractals for
cancer risk assessmentÓ
Pakistan Journal of Statistic, Vol. 30(4), 439-454.
Stehl ́ők M., Hermann, P., and Nicolis,
O.(2016) Fractal based cancer modelling,
Revstat, 14, 2, 139-155
Stehl ́ők, M. (2016). On convergence of topological aggregation functions. Fuzzy
Sets and Systems, 287:4856.