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The Kaplan–Meier estimator, [1] [2] also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment.
The Kaplan–Meier estimator can be used to estimate the survival function. The Nelson–Aalen estimator can be used to provide a non-parametric estimate of the cumulative hazard rate function. These estimators require lifetime data.
The problem with measuring overall survival by using the Kaplan-Meier or actuarial survival methods is that the estimates include two causes of death: deaths from the disease of interest and deaths from all other causes, which includes old age, other cancers, trauma and any other possible cause of death. In general, survival analysis is ...
The survival function is also known as the survivor function [2] or reliability function. [3] The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime ...
The logrank test is based on the same assumptions as the Kaplan-Meier survival curve—namely, that censoring is unrelated to prognosis, the survival probabilities are the same for subjects recruited early and late in the study, and the events happened at the times specified. Deviations from these assumptions matter most if they are satisfied ...
Kaplan-Meier curve illustrating overall survival based on volume of brain metastases.Elaimy et al. (2011) [6] In its simplest form, the hazard ratio can be interpreted as the chance of an event occurring in the treatment arm divided by the chance of the event occurring in the control arm, or vice versa, of a study.
Paul Meier (July 24, 1924 – August 7, 2011) [1] was a statistician who promoted the use of randomized trials in medicine. [2] [3]Meier is known for introducing, with Edward L. Kaplan, the Kaplan–Meier estimator, [4] [5] a method for measuring how many patients survive a medical treatment from one duration to another, taking into account that the sampled population changes over time.
When the covariates are omitted from the analysis, the maximum likelihood boils down to the Kaplan-Meier estimator of the survivor function. [6] Another way to model discrete duration data is to model transitions using binary choice models. [7]