Survival Analysis

Survival analysis models the time until an event of interest. The event need not be death: it can be machine failure, product return, account cancellation, or recovery after treatment. A key feature is censoring. For example, a study may end while a participant has not had the event; the person’s exact event time is unknown, but event-free follow-up up to that point still matters. Excluding such observations can bias estimates. The Kaplan–Meier estimator provides a nonparametric estimate of the survival function, the probability that an event has not occurred by a given time. NIST describes it for failure-time data with censoring, while CDC Epi Info notes that survival analysis differs from ordinary methods because incomplete observations are censored. The log-rank test compares survival curves under assumptions; Cox proportional-hazards models relate covariates to the hazard rate, not directly to a person’s probability of surviving. Each method answers a distinct question. Interpretation depends on clear time origin, event definition, follow-up, and censoring. Standard Kaplan–Meier analysis relies on censoring being non-informative under the analysis; if people leave because their risk changed, treating them as ordinary censored cases may mislead. Competing risks can also make an event impossible after another event occurs. Report the number at risk, uncertainty intervals, and assumptions, and avoid comparing a median survival time without context. This guide is educational and is not medical advice or an individualized prognosis.