Prediction of long term stability by extrapolation

This paper studies the possibility of using the survival function to predict long term stability by extrapolation. The survival function is a function of the initial coordinates and is the number of turns a particle will survive for a given set of initial coordinates. To determine the difficulties in extrapolating the survival function, tracking studies were done to compute the survival function. The survival function was found to have two properties that may cause difficulties in extrapolating the survival function. One is the existence of rapid oscillations, and the second is the existence of plateaus. It was found that it appears possible to extrapolate the survival function to estimate long term stability by taking the two difficulties into account. A model is proposed which pictures the survival function to be a series of plateaus with rapid oscillations superimposed on the plateaus. The tracking studies give results for the widths of these plateaus and for the seperation between adjacent plateaus which can be used to extrapolate and estimate the location of plateaus that indicate survival for longer times than can be found by tracking.Comment: 23 pages, 15 figure

Semi-Competing Risks on A Trivariate Weibull Survival Model

A setting of a trivairate survival function using semi-competing risks concept is proposed. The Stanford Heart Transplant data is reanalyzed using a trivariate Weibull distribution model with the proposed survival function

Preimplantation biopsy predicts delayed graft function, glomerular filtration rate and long-term graft survival of transplanted kidneys

Background The predictive value of preimplantation biopsies for long-term graft function is often limited by conflicting results. The aim of this study was to evaluate the influence of time-zero graft biopsy histological scores on early and late graft function, graft survival and patient survival, at different time points. Methods We retrospectively analyzed 284 preimplantation biopsies at a single center, in a cohort of recipients with grafts from live and deceased donors (standard and nonstandard), and their impact in posttransplant renal function after a mean follow-up of 7 years (range 1–16). Implantation biopsy score (IBS), a combination score derived from 4 histopathological aspects, was determined from each sample. The correlation with incidence of delayed graft function (DGF), creatinine clearance (1st, 3rd and 5th posttransplant year) and graft and patient survival at 1 and 5 years were evaluated. Results Preimplantation biopsies provided somewhat of a prognostic index of early function and outcome of the transplanted kidney in the short and long term. In the immediate posttransplantation period, the degree of arteriolosclerosis and interstitial fibrosis correlated better with the presence of DGF. IBS values between 4 and 6 were predictive of worst renal function at 1st and 3rd years posttransplant and 5-year graft survival. The most important histological finding, in effectively transplanted grafts, was the grade of interstitial fibrosis. Patient survival was not influenced by IBS. Conclusions Higher preimplantation biopsy scores predicted an increased risk of early graft losses, especially primary nonfunction. Graft survival (at 1st and 5th years after transplant) but not patient survival was predicted by IBS

Survival as a Function of Life Expectancy

It is well known that life expectancy can be expressed as an integral of the survival curve. The reverse - that the survival function can be expressed as an integral of life expectancy - is also true.force of mortality, life expectancy, life table, stationary population, survival function