Survival analysis
Survival analysis studies time until an event, such as death, recovery, relapse or failure.
Survival function
For event time \(T\),
\[S(t)=P(T>t).\]Hazard
The hazard describes the instantaneous event rate among individuals who have survived to time \(t\):
\[h(t)=\lim_{\Delta t\to0}\frac{P(t\le T<t+\Delta t\mid T\ge t)}{\Delta t}.\]Censoring
If an individual has not experienced the event before observation ends, the exact event time may be unknown. Survival methods can incorporate such right-censored observations under appropriate assumptions.
Key idea. Survival analysis uses both whether an event occurs and how long it takes to occur.