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

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.

Monte-Carlo Simulation on the Failure of Fiber in a Single Filament Composite

A Monte-Carlo method is used to simulate gradual fracture of fiber in a single filament composite with the increase of virtual stress. A simple computational algorithm is developed to judge where breaking point will happen in the composite and a probability model based on Weibull- distribution is designed to calculate the average fragment length by producing stable and uniform random number in (0, 1). Compared to the published experiment results, the simulating average fragment length is quite perfect.

Approaching Complexity: Hyperthermia Dose and Its Possible Measurement in Oncology

A heuristic stochastic solution of the Pennes equation is developed in this paper by applying the self-organizing, self-similar behaviour of living structures. The stochastic solution has a probability distribution that fits well with the dynamic changes in the living objects concerned and eliminates the problem of the deterministic behaviour of the Pennes approach. The solution employs the Weibull two-parametric distribution which offers satisfactory delivery of the rate of temperature change by time. Applying the method to malignant tumours obtains certain benefits, increasing the efficacy of the distortion of the cancerous cells and avoiding doing harm to the healthy cells. Due to the robust heterogeneity of these living systems, we used thermal and bioelectromagnetic effects to distinguish the malignant defects, selecting them from the healthy cells. On a selective basis, we propose an optimal protocol using the provided energy optimally such that molecular changes destroy the malignant cells without a noticeable effect on their healthy counterparts.