Short Analysis: Analysis Of The Kaplan-Meier Analysis

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The Kaplan–Meier estimator is a product limit estimator that is used for estimating the survival function from lifetime data [24]. The aim of this estimator is to estimate a population of patients’ survival curve from a sample. This estimator is used in addition to the Receiver-operator characteristic ROC curve to evaluate the performance of the prediction model [25-27]. Of course, if every patient is followed until death, the curve may be estimated simply by computing the fraction surviving at each time. However, in most medical studies patients tend to drop out, become lost to follow up, move away, etc. The Kaplan-Meier analysis allows estimation of survival over time, even when patients drop out or are studied for different lengths of time. …show more content…

Patients who have died, dropped out, or not reached the time yet are not counted as “at risk.” On the other hand, patients who are lost are considered “censored” and are not counted in the denominator. The probability of surviving to any point is estimated from cumulative probability of surviving each of the preceding time intervals (calculated as the product of preceding probabilities). Although the probability calculated at any given interval isn’t very accurate because of the small number of events, the overall probability of surviving to each point is more accurate. Thus the plot of the Kaplan–Meier estimate of the survival function is a series of horizontal steps of declining magnitude which, when a large enough sample is taken, approaches the true survival function for that population. The value of the survival function between successive distinct sampled observations ("clicks") is assumed to be constant. If a patient withdraws from a study, i.e. is lost from the sample before the final outcome is observed then small vertical tick-marks on the plot indicate losses, where a patient's survival time has been right-censored. When no truncation or censoring occurs, the Kaplan–Meier curve is the complement of the empirical distribution

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