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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.
This topic is called reliability theory, reliability analysis or reliability engineering in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time?
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 ...
That is, 97% of subjects survive more than 2 months. Survival function 2. Median survival may be determined from the survival function: The median survival is the point where the survival function intersects the value 0.5. [4] For example, for survival function 2, 50% of the subjects survive 3.72 months. Median survival is thus 3.72 months.
As a counterpart of the Kaplan–Meier curve, which is used to describe the time to a terminal event, recurrent event data can be described using the mean cumulative function, which is the average number of cumulative events experienced by an individual in the study at each point in time since the start of follow-up.
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.
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
Edward Lynn Kaplan (May 11, 1920 – September 26, 2006) [1] was a mathematician most famous for the Kaplan–Meier estimator, [2] developed together with Paul Meier. Biography [ edit ]