Kaplan-Meier survival analysis

The Kaplan-Meier estimator is a nonparametric method for estimating the survival function — the probability of surviving beyond each observed event time — from censored time-to-event data. At each event time, the estimate is updated as the ratio of subjects remaining at risk minus those who experienced the event, multiplied forward as a product-limit. The resulting step function graphically displays survival over follow-up and allows group comparisons via the log-rank test. Key assumptions include that censoring is non-informative (i.e., subjects who leave the study do not systematically differ in prognosis) and that survival probability is independent across individuals. The median survival — where the curve crosses 50% — is the standard summary statistic; mean survival is rarely used because it requires the curve to reach zero.