Parametrization of Survival Measures, Part I: Consequences of Self-Organizing

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.