Math 2.0

Statistics Definition

Survival analysis

Builds on Survival functionHazard functionCensoringStatistical inference

Definition

Survival analysis is the branch of statistical inference whose data are times to an event. Its setting is a nonnegative random variable TT, the event time, together with observations of TT that may be censored. Its aims are to estimate the survival function S(t)=P(T>t)S(t) = P(T > t) and the hazard function of TT. It also compares them between groups and models how they depend on covariates.

Remarks

The data of subject ii usually take the form (t~i,δi,xi)(\tilde t_i, \delta_i, x_i), where xix_i is a vector of covariates. Here t~i=min⁡(Ti,Ci)\tilde t_i = \min(T_i, C_i) is the observed time, CiC_i is a censoring time, and δi=1\delta_i = 1 if Ti≤CiT_i \le C_i and 00 otherwise.

Example: estimating the fraction of light bulbs that still work after 10001000 hours, when the test is stopped at 15001500 hours, is a survival analysis problem. The bulbs still working at 15001500 hours give right-censored times.

Non-example: estimating the mean weight of the bulbs is not survival analysis, since the quantity of interest is not a time to an event.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Censoring, concept, no evidence levelCensoringconceptHazard function, concept, no evidence levelHazard functionconceptStatistical inference, concept, no evidence levelStatistical inferenceconceptSurvival function, concept, no evidence levelSurvival functionconceptSurvival analysis, definition, no evidence levelSurvival analysisdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Censoring concept
  2. Hazard function concept
  3. Statistical inference concept
  4. Survival function concept
  5. Survival analysis definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Survival_analysis
About this page
TagS6VR0CVZ86
URIm2://S6VR0CVZ86
Kinddefinition
WritingW0 stub
MSC62N01, 62N02, 62P10
DefinesSurvival analysis
UsesSurvival function, Hazard function, Censoring, Statistical inference

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