An Empirical Saddlepoint Approximation Based Method for Smoothing Survival Functions Under Right Censoring

• Activity Number: 106 - Empirical Transforms, Saddlepoint Approximations, and Risk Assessment with Some Applications
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Adao Trindade* and Pratheepa Jeganathan and Noroharivelo Randrianampy and Robert Paige
• Companies: Texas Tech University and Stanford University and HECMMA and Missouri University of Science and Technology
• Keywords: Moment generating function ; Kaplan-Meier estimator ; tail-completion ; lifetime data

Abstract

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. Using tools from the theory of empirical processes, uniform consistency, weak, and strong convergence results are established for this modified version of the empirical MGF based on KM weights. 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.