Consistency of the Kaplan-Meier Estimator of the Survival Function in Competiting Risks
Didier Alain Njamen Njomen1, *, Joseph Wandji Ngatchou2
Identifiers and Pagination:Year: 2018
First Page: 1
Last Page: 17
Publisher Id: TOSPJ-9-1
Article History:Received Date: 23/11/2017
Revision Received Date: 26/02/2018
Acceptance Date: 25/03/2018
Electronic publication date: 30/04/2018
Collection year: 2018
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this article, we only focus on the probability distributions of the breakdown time whose causes are known, and we consider a partition of the observations into subgroups according to each of the causes as defined in Njamen and Ngatchou . By adapting the stochastic processes developed by Aalen [2, 3], we derive a Kaplan-Meier  nonparametric estimator for the survival function in competiting risks.
Result & Discussion:
In a region where there is at least one observation, we prove on one hand that this new nonparametric estimator is unbiased in competiting risk and on the other hand, using the Lenglart inequality, we establish its uniform consistency in competiting risks.