Survival Analyis and Kaplan Meier method of Survival Analysis

Survival analysis is mathematical modeling of time to event analysis, which in simple words, means the methods to analyse the timing of events, e.g., deaths or failures.

In oncology the long term outcome of all interventions are mostly analyzed by time to event analysis, where treatment failure is either perceived as local failure, distant failure or death. An individual treatment/ treatment protocol is perceived superior than an alternative one if the number of failures occurring in a given time frame are less than the alternative one or are occurring later than the alternative treatment. Such type of nonparametric data can be analyzed using a survival analysis.

There are various methods for survival analysis, but the two most commonly used methods are the Life table/ acturian method and the Kaplan Meier survival analysis

Life table analysis described by John Graunt andWilliam Petty in 17th century, who pioneered the study of mortality, is based on the basic assumption of expectation of life of a particular population for a given period.

Kaplan Meier analysis first described in 1958, (Kaplan E L & Meter P. Nonparanietric estimation from incomplete observations.I. Amer. Statist. Assn. 53:457-81, 1958) also known as product imit estimator, estimates the survival fraction from life table data. Here the time to event is plotted in a stepwise manner , where is event represents a vertical fall of a step. Survival fraction is estimated for a small time unit defined by subsequent events. the advantage of this method it takes account of all those patients who are lost to follow up or entered late into the study (censored). The final survival is the cumulative survival , that is the product of all survival fractions.

for e.g.

suppose at the begining of study ( that is the start of time frame ) 100 patients were surviving. At the end of 1 year 20 patients died and another 10 lost to follow up. Again at the end of 2nd year another 10 patients died.

so the survival by simple mathematics at the end of 2 yrs = 60/100= 60%.

however this does not take into account of the patients who were lost to follow up. By kaplan meier analysis method (asuming that all deaths ocurred at same time at the end of years) the survival at 2 years will be

time 1yr; SF = 80/100=0.8/80%
time 2yr ; SF = 60/70=0.857/85.7%, so cumulative survival = 0.8x0.857=0.686/68%

so instead of 60% the survival at 2 years came out to be 68%. logically this sounds better since actual deaths were only 30. but it is also not 70% since we do not know what becomes of those 10% that were lost to follow up , hence it is lesser than 70% but more than 60%.

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