title: A Mass Redistribution Algorithm for Right Censored and Left Truncated Time to Event Data.
abstract: 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) estimator for the cumulative incidence function.
authors.affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA,  matxxz@langate.gsu.edu , .
authors.forename: Xu
authors.initials: X
authors.lastname: Zhang
authors.forename: Mei-Jie
authors.initials: MJ
authors.lastname: Zhang
authors.forename: Jason
authors.initials: J
authors.lastname: Fine