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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 distribution of failure times is the probability density function (PDF), since time can take any positive value. In equations, the PDF is specified as f T . If time can only take discrete values (such as 1 day, 2 days, and so on), the distribution of failure times is called the probability mass function .
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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.
It also estimates the tail probability of the Kolmogorov–Smirnov statistic. The inequalities above follow from the case where F corresponds to be the uniform distribution on [0,1] [ 6 ] as F n has the same distributions as G n ( F ) where G n is the empirical distribution of U 1 , U 2 , …, U n where these are independent and Uniform(0,1 ...
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 ...