Kaplan–Meier estimate

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A procedure for estimating the survivor function from observations of lifetimes (of people, machine components, etc.) when some observations are censored (e.g. people move away from the observation site, or functioning components are removed before the end of the experimental period). The estimate is calculated as follows. First, order the data by length of lifetime. Suppose there are m distinct lifetimes (where, for example, people alive at the time of calculation are given their current lifetime). Let t(j) be the jth of these ordered lifetimes, let nj individuals have lifetimes of t(j) or more, and let dj individuals have lifetimes of exactly t(j). The Kaplan–Meier estimate of the survivor function is given by . The corresponding estimator has variance estimated by the Greenwood formula. Closely related to the Kaplan–Meier estimate is the Nelson–Aalen estimate of the cumulative hazard rate, given by .

Subjects: Probability and Statistics.

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