RESEARCH ARTICLE
Consistency of the Kaplan-Meier Estimator of the Survival Function in Competiting Risks
Didier Alain Njamen Njomen1, *, Joseph Wandji Ngatchou2
1 Department of Mathematics and Computer Sciences, Faculty of Science, University of Maroua, Maroua, Cameroon
Article Information
Identifiers and Pagination:
Year: 2018Volume: 9
First Page: 1
Last Page: 17
Publisher Id: TOSPJ-9-1
DOI: 10.2174/1876527001809010001
Article History:
Received Date: 23/11/2017Revision Received Date: 26/02/2018
Acceptance Date: 25/03/2018
Electronic publication date: 30/04/2018
Collection year: 2018
© 2018 Njomen et al.
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.
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.
Abstract
Introduction:
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 [1]. By adapting the stochastic processes developed by Aalen [2, 3], we derive a Kaplan-Meier [4] 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.
Keywords: Censored data, Counting process, Survival function, Competiting risks, Kaplan-Meier estimators, Bias of an estimator, Uniform consistency.
