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
2 Institut Elie Cartan de Lorraine, University of Lorraine, Nancy, France

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© 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: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics and Computer Sciences, Faculty of Science, University of Maroua, Maroua, Cameroon; Tel: +237 675 27 65 20; E-mails: /



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.