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Abstract:
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The Kaplan-Meier (KM) estimator is a commonly used non-parametric procedure for estimating survival functions. However, KM only defines the approximate probability of observed failure times, and may not deliver a proper density function if the largest observation is right censored. In addition, existing smoothing methods based on KM also assume that the largest observation is not censored. To alleviate these issues, we devise a method for smoothing KM survival functions based on an empirical saddlepoint approximation. The method inverts the moment generating function (MGF) defined through a Riemann-Stieltjes integral of the empirical cumulative distribution function with KM weights and exponential right-tail completion. The performance of the methodology is examined in simulation studies, which demonstrates that the proposed empirical saddlepoint approximation method is faster and more accurate than existing methods for smoothing survival functions. The R scripts were written to implement the new method, and R is used for all the simulation studies.
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