Survival analysis
This section introduces the survival analysis concept and the most popular techniques related to this subject  they are detailed in the following:
0. Survival analysis
Survival analysis corresponds to a set of statistical approaches used to investigate the time that it takes for an event of interest to occur (timetoevent data). It is used in biology (for patients’ survival time analyses, time from first heart attack to the second, etc), sociology (for “eventhistory analysis”) and in engineering (for “failuretime analysis”), for instance (1,2).
1. Cox model
A Cox model [also Cox (proportional hazards) regression model] is a statistical technique for exploring the relationship between the survival of a patient and several explanatory variables. A Cox model builds a survival function which gives a probability of a certain event at a particular time t  the hazard (or risk) of death for an individual, given their prognostic variables. Once a model is built from the observed values, it can then be used to make predictions for new inputs. Cox models are able to deal with censored data (1,2).
2. Log rank test
The logrank test (MantelCox test) is a nonparametric hypothesis test to compare survival distributions from two samples, i.e. testing the null hypothesis that there is no difference between the populations in the probability of an event (i.e. death) at any time point. It is often used in clinical trials to compare survival experience for two groups of individuals, as it can handle censored or right skewed data. It could be used to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event. An extension of the logrank test exists (MaxCombo) which tends to be more robust in a context of nonproportional hazards (1,2).
3. Kaplan Meier estimator
The Kaplan–Meier estimator is a nonparametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment. A plot of the Kaplan–Meier estimator (KM curve) is a series of declining horizontal steps which, with a large enough sample size, approaches the true survival function for that population. An important advantage of the Kaplan–Meier curve is that the method can take into account some types of censored data, particularly rightcensoring, which occurs if a patient withdraws from a study, is lost to followup or is alive without event occurrence at last followup. On the plot, small vertical tickmarks state individual patients whose survival times have been rightcensored. (1,2)
4. Random Survival Forest
A random survival forest is a nonparametric ensemble method for the analysis of right censored survival data, built as a timetoevent extension of random forests for classification. The method can handle multiple covariates, noise covariates, as well as complex, nonlinear relationships between covariates without need for prior specification (1,2)
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