Empirical Saddlepoint Approximations (ESPA) for Smoothing Survival Functions Under Right Censoring

The KM estimator is a commonly used nonparametric estimator of a survival function, but the KM estimator only defines the approximate probability of observed failure times and may not define a proper density function if the largest observation is right-censored.


We can apply this method for several event-time data from the clinical research to estimate a smooth survival curve.


We define the empirical moment generating function (MGF) of the tail-completed density function based on the KM estimator, then, using the saddlepoint method, accurately approximate a smooth survival function. Before using the saddlepoint method for this purpose, however, we establish the convergence results of the modified version of the empirical MGF based on the KM estimator using the M-estimation and multivariate delta method.