The Kaplan-Meier integral in the presence of covariates: A review

Abstract

In a series of papers, Winfried Stute introduced and studied the Kaplan-Meier integral as an estimator of parameters of the joint distribution of survival times and covariates based on right censored survival times. We present a review of this work and show that his estimator has an inverse probability of censoring weighting (IPCW) representation. We further investigate large sample bias and efficiency. As a central application in a biostatistical context, Kaplan-Meier integrals are used to estimate transition probabilities in a non-Markov illness-death model. We extend already existing approaches by introducing a novel estimator that also works in the presence of additional left truncation. This application illustrates that Winfried Stute's work can successfully be used to develop inferential statistical methods in complex survival models.