Abstract
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 self-organizing 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. 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.
Highlights
Weibull distribution function (WF) parametrization needs two independent parameters, which could be obtained from the median and mean values of Kaplan-Meier non-parametric estimate (KM) estimate, which makes an easy parametric approximation of the KM plot
We use a large number of patients (1180 individuals), with various tumors treated by numerous standard therapies, but having one thing in common: they are treated by complementary modulated electro-hyperthermia, when the standard treatment fail to deliver the desirable results, [123] [124]; Figure 10
The self-organizing and self-similarity with their consequences determine the strict connection of the parametric approach well with the experimental non-parametric observations
Summary
Szasz tempt to minimize the actual energy and maximize the entropy in the actual processes. In this sense, life follows the basic thermodynamic laws: the living process continuously “burns” the incoming “nutrition”. The energy-pump of the incoming sun-energy makes the difference: creates original gradients which are later divided into other inhomogeneities by spontaneous processes. Life process tries to diminish the working energy of the sunlight by increasing the overall entropy of the environment. Living process lowers the electron energy by the oxidation producing outgoing (waste) final “products”. The gradual loss of electron energy of the “nutrition” molecules is the energy to sustain life. The living process is a dissipative entropy producer. Szentgyorgyi states “Life is nothing but an electron looking for a place to rest” [1]
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