Survival Analysis is a field of statistics which traditionally deals with the death of biological organisms and the failure of mechanical systems. This branch is also called reliability theory or reliability analysis in engineering. Death or failure is called an "event" in survival analysis literature, and so models of death or failure are sometimes called time-to-event models. Survival Analysis includes numerous statistical methods for analyzing the occurrence and timing of events. These methods are mainly concerned with determining the time between the entry to a study and exit (survival time or failure time). Originally the analysis was designed to estimate the time from treatment until death, hence the name. Currently Survival Analysis is applicable in many other areas besides mortality (see for example Collett 1994).

A frequent problem in medical, biological, or engineering research is to determine whether certain continuous independent variables are correlated with the survival/failure time. Most often the goal of Survival Analysis is to characterize the distribution of the survival time for a given population, to compare this survival time among different groups, or to study the relationship between the survival time and other variables. There are two main reasons why this problem cannot be solved using multiple regression techniques: the time-dependent covariates (survival/failure times) often follow an exponential or Weibull distribution, and there is the problem of censoring (some observations are incomplete). Several different methods can be used for analyzing such data: the Kaplan-Meier estimators, exponential or log-normal regression, semi-parametric regression. This chapter deals with the most popular semi-parametric model proposed by Cox 1972 (the proportional hazards model) and two nonparametric survival models: the Kaplan-Meier and Life-Table estimators. All these models are implemented in AdvancedMiner.