# Survival Function

## Definitions

### Health Economics

- In some trials, the outcome is the difference in the distributions of survival times of an experimental and a control group. Survival functions (or curves) plot the proportion of all individuals in a population or sample surviving at a variety of dates. The term 'survival' sounds like life-and-death, which it sometimes is, but survival curves can be used to study times required to reach any well-defined endpoint (e.g. discharge from hospital, return to work). The analysis of survival data in trials can pose problems because some observations are censored as the event of interest has not occurred for all patients over the study period. For example, when patients are re cruited over, say three years, one recruited at the end of the study may be alive at follow-up after a year, whereas one recruited at the start may have died after two years. The patient who died has a longer observed survival than that for the one who still survives and whose ultimate survival time may be unknown. The Kaplan-Meier method is a method of estimating the proportion of patients surviving to any given date, which is also the estimated probability of survival to that time for a member of the population from which the sample is drawn. A survival curve (Kaplan-Meier curve) plots the estimated probability of survival for a sample of data (not the actual proportion surviving) against time on the horizontal axis in such a fashion that the censoring is allowed for and the maximum use is made of the available data.
- synonymSurvival Curve (written as
*survival function*)