Nelson-Aalen and Kaplan-Meier Estimators in Competing Risks

Nelson–Aalen Estimator

The Nelson–Aalen estimator is a nonparametric estimator which may be used to estimate the cumulative hazard rate function from censored survival data (see Survival Distributions and Their Characteristics). Since no distributional assumptions are needed, one important use of the estimator is to check graphically the fit of parametric models, and this is the reason why it was originally introduce...

Kaplan–Meier Estimator

The Kaplan–Meier estimator is a nonparametric estimator which may be used to estimate the survival distribution function from censored data. The estimator may be obtained as the limiting case of the classical actuarial (life table) estimator, and it seems to have been first proposed by Böhmer [2]. It was, however, lost sight of by later researchers and not investigated further until the importa...

Kaplan-Meier Type Estimators for Linear Contact Distributions

The linear contact distribution function is shown to be continuously diieren-tiable for any stationary random closed set, which implies the existence of a continuous density and hazard rate. Moreover, it is proved that the density is monotone decreasing. When the linear contact distribution function is estimated from observations in a bounded window, the distance to the set of interest from a x...

SEMIPARAMETRIC ESTIMATORS IN COMPETING RISKS REGRESSION by

Overestimation of the probability of death on peritoneal dialysis by the Kaplan-Meier method: advantages of a competing risks approach

BACKGROUND In survival analysis, patients on peritoneal dialysis are confronted with three different outcomes: transfer to hemodialysis, renal transplantation, or death. The Kaplan-Meier method takes into account one event only, so whether it adequately considers these different risks is questionable. The more recent competing risks method has been shown to be more appropriate in analyzing such...