ABSTRACT
The analysis of survival data usually starts with the estimation of the survival function and related summary quantities. Hypotheses testing for the comparison of the survival functions of two or more sub-populations is often of prime interest. This is typically the case in a randomized clinical trial with a time-to-event outcome, where the interest is to identify whether the experimental treatment leads to a longer time-to-event for the patients in this treatment arm compared to the standard treatment. Event-times are, by definition, positive and often present a skewed distribution. Therefore usual standard distribution, such as the normal distribution, can not be used. Amongst the non-negative parametric density, the most popular ones in survival analysis are the Exponential, Weibull, or Log-normal distribution. Specific non-parametric estimators of the survival function which allows to take into account the partial information available from the censored observations have therefore been proposed.
