A recursive formula for the Kaplan-Meier estimator with mean constraints and its application to empirical likelihood

Mai Zhou, Yifan Yang

Abstract: The Kaplan–Meier estimator is very popular in analysis of survival data. However, it is not easy to compute the ‘constrained’ Kaplan–Meier. Current computational method uses expectation-maximization algorithm to achieve this, but can be slow at many situations. In this note we give a recursive computational algorithm for the ‘constrained’ Kaplan–Meier estimator. The constraint is assumed given in linear estimating equations or mean functions. We also illustrate how this leads to the empirical likelihood ratio test with right censored data. Speed comparison to the EM based algorithm favours the current procedure.