Survival analysis

Survival analysis is a branch of statistics that deals with analysis of time duration until one or more events happen, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer 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 these questions, researchers commonly use a tool called a survival function, denoted S(t), which is defined as the probability that the time to event is later than some specified time t. The survival function can be estimated from either an established parametric survival distribution, a nonparametric estimator like the Kaplan-Meier estimator, or semi-parametric models like Cox proportional hazards model.

History

Survival analysis has been a topic of interest since the 18th century, with early work by Benjamin Gompertz and Thomas Bayes. The field has since expanded to include not only the study of survival rates for biological organisms, but also the analysis of failure rates in mechanical systems, such as those used in engineering.

Applications

Survival analysis has been used in a variety of fields, including:

• Biology: Survival analysis can be used to model the lifetimes of organisms, with applications in fields such as epidemiology and gerontology.
• Engineering: In reliability engineering, survival analysis can be used to model the time until failure of systems.
• Economics: Duration analysis, a subfield of survival analysis, is used in economics to model the time until events such as job changes or the end of economic recessions.
• Sociology: Event history analysis, another subfield of survival analysis, is used in sociology to model the time until events such as marriage or divorce.

See also

• Censoring (statistics)
• Hazard ratio
• Survival function
• Life table
• Proportional hazards models
• Accelerated failure time model
• Log-rank test

Survival_analysis

• Kaplan-Meier by treatment in AML
  Kaplan-Meier by treatment in AML
• Cox proportional hazards regression output for melanoma data set
  Cox proportional hazards regression output for melanoma data set
• Histograms of melanoma thickness
  Histograms of melanoma thickness
• Cox PH output for melanoma with thickness
  Cox PH output for melanoma with thickness
• Survival tree for prostate cancer
  Survival tree for prostate cancer
• Data resampling for discrete-time survival models
  Data resampling for discrete-time survival models