---
tag: 443ZWDX88P
kind: concept
name: Survival analysis
msc: [62N01, 62N02, 62P10]
sources:
  - url: https://en.wikipedia.org/wiki/Survival_analysis
same_as:
  wikidata: Q543310
  wikipedia: Survival analysis
---

## Summary

Survival analysis is the part of statistics that studies the time until an event happens.
Examples of events are death, relapse of a disease or failure of a machine.
Its central objects are the [[survival function|QTM1HZM53Q]] and the [[hazard function|Y959NKQ3XW]] of the event time.
Its typical difficulty is [[censoring|MY8ZZP84NP]].
For some subjects the event is not observed during the study, and only a lower bound for their time is known.
Standard tools include the [[Kaplan–Meier estimator|B7AJ8RWZRC]], the [[log-rank test|F6CT1YXZ0G]] and the [[proportional hazards model|N029V3JX60]].

## Explanations

### L1 human

A clinical trial follows patients for five years and records when each one has a relapse.
Some patients have no relapse before the trial ends, and some move away; for them we only know that the relapse came later than their last visit.
Survival analysis uses these incomplete records correctly instead of throwing them away.
It answers questions such as "what fraction of patients is still free of relapse after two years?" and "does the new drug delay relapse?".
In engineering the same methods are called reliability analysis.