A mass redistribution algorithm for right-censored and left-truncated time to event data

Failure times are often right censored and left truncated. In this paper we give a mass redistribution algorithm for right-censored and/or left-truncated failure time data. We show that this algorithm yields the Kaplan–Meier estimator of the survival probability. One application of this algorithm in modeling the subdistribution hazard for competing risks data is studied. We give a product-limit estimator of the cumulative incidence function via modeling the subdistribution hazard. We show by induction that this product-limit estimator is identical to the left-truncated version of Aalen–Johansen [1978. An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics 5, 141–150] estimator for the cumulative incidence function.