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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.
In the latter case, the reliability function is denoted R(t). Usually one assumes S(0) = 1, although it could be less than 1 if there is the possibility of immediate death or failure. The survival function must be non-increasing: S(u) ≤ S(t) if u ≥ t. This property follows directly because T>u implies T>t. This reflects the notion that ...
I beleive that an example calculation is necessary for a comprehensive description of the Kaplan-Meier estimate. However, I agree that the section is long, and it need not be in the middle of the article; it can be moved to the end for those readers who wish to see the example calculation.
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.
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 ...
This is useful to estimate the failure rate of a system when individual components or subsystems have already been tested. [ 18 ] [ 19 ] Adding "redundant" components to eliminate a single point of failure may thus actually increase the failure rate, however reduces the "mission failure" rate, or the "mean time between critical failures" (MTBCF).
An early paper to use the Kaplan–Meier estimator for estimating censored costs was Quesenberry et al. (1989), [3] however this approach was found to be invalid by Lin et al. [4] unless all patients accumulated costs with a common deterministic rate function over time, they proposed an alternative estimation technique known as the Lin ...
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