Editing Survival analysis (section)

{{short description|Branch of statistics}}
{{more citations needed|date=April 2021}}
'''Survival analysis''' is a branch of [[statistics]] for analyzing the expected duration of time until one event occurs, such as death in [[biological organism]]s and failure in mechanical systems.<ref>{{Cite journal |last1=Clark |first1=T G |last2=Bradburn |first2=M J |last3=Love |first3=S B |last4=Altman |first4=D G |date=2003-07-15 |title=Survival Analysis Part I: Basic concepts and first analyses |journal=British Journal of Cancer |language=en |volume=89 |issue=2 |pages=232–238 |doi= 10.1038/sj.bjc.6601118|pmid=12865907 |pmc=2394262 }}</ref> This topic is called '''reliability theory''', '''reliability analysis''' or [[reliability engineering]] in [[engineering]], '''duration analysis''' or '''duration modelling''' in [[economics]], and '''event history analysis''' in [[sociology]]. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of [[survival]]?

To answer such questions, it is necessary to define "lifetime". In the case of biological survival, [[death]] is unambiguous, but for mechanical reliability, [[failure]] may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of degree, or not otherwise localized in [[time]]. Even in biological problems, some events (for example, [[myocardial infarction|heart attack]] or other organ failure) may have the same ambiguity. The [[theory]] outlined below assumes well-defined events at specific times; other cases may be better treated by models which explicitly account for ambiguous events.

More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an "event" in the survival analysis literature – traditionally only a single event occurs for each subject, after which the organism or mechanism is dead or broken. ''Recurring event'' or ''repeated event'' models relax that assumption. The study of recurring events is relevant in [[systems reliability]], and in many areas of social sciences and medical research.