Kaplan-Meier survival function

The Kaplan-Meier estimator (also known as the product-limit estimator) is a non-parametric statistic used to estimate the empirical survival function.

The Kaplan-Meier survival probability at failure time t(f) is the probability of surviving past the previous failure time t(f-1) multiplied by the conditional probability of surviving past time t(f) given survival to at least time t(f).

A plot of the survival probabilities at each ordered failure time produces an empirical survival function (or survival curve) - a step-function starting with a horizontal line at a survival probability of 1 and a step down at each failure time. A censored observation does not produce any step in the survival function, but it is sometimes useful to denote such observations.

A key statistic for describing the survival function are the quartiles (25th, 50th, and 75th quantiles of the survival function). Another statistic is the mean survival time, the area under the survival curve. It is often less useful as many survival functions do not drop to 0 (due to some observations being censored at the end of the study). A workaround, particularly when comparing multiple survival functions, is to restrict the area under the curve to the interval 0, t, which is common to all the survival curves.