Lifetime analyses frequently apply a parametric functional
description from measured data of the
Kaplan-Meier non-parametric estimate (KM) of the
survival probability. The cumulative Weibull
distribution function (WF) is the primary choice to
parametrize the KM. but some others (e.g.
Gompertz, logistic functions) are also widely applied.
We show that the cumulative two-parametric
Weibull function meets all requirements. The Weibull
function is the consequence of the general selforganizing behavior of the
survival, and consequently shows self-similar death-rate as a function of
the time. The ontogenic universality as well as the universality
of tumor-growth fits to WF. WF
parametrization needs two independent parameters, which
could be obtained from the median and
mean values of KM estimate, which makes an easy
parametric approximation of the KM plot. The
entropy of the distribution and the other entropy
descriptions are supporting the parametrization
validity well. The goal is to find the most appropriate
mining of the inherent information in KM-plots.
We show clinical examples of oncological hyperthermia
treatment, evaluated by single-arm study. The
method which we chosen is the modulated
electrohyperthermia (mEHT, oncothermia ®) which is
applied in the final stages of the cancer, and no
conventional treatment as control is available in many
studies. We show the two-parameter WF fits to the
non-parametric KM survival curve in a real study
of 1180 cancer patients offering satisfactory
description of the clinical results. Two of the 3
characteristic parameters of the KM plot (namely the
points of median, mean or inflection) are enough
to reconstruct the parametric fit, which gives support
of the comparison of survival curves of different
patient’s groups. Objective
in this chapter is to find a parametric description of overall survival, which
fits the selforganized processes and is able to show the inherent information
of survival measurements of cancer patients in
advanced cases, when the curative conventional and evidence-based proven
therapies fail.
Author
(s) Details
Dr. O. Szasz
Biotechnics Department, Faculty of Mechanical Engineering, St.
Istvan University, Hungary.
A. M. Szasz
Division of Oncology, Department of Internal Medicine and Oncology,
Semmelweis University, Budapest, Hungary
Dr. G. P. Szigeti
Innovation Center, Semmelweis University, Budapest, Hungary
Prof. Dr. A. Szasz
Biotechnics Department, Faculty of Mechanical Engineering, St. Istvan
University, Hungary.
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