Journal of Advanced Statistics

Study of the Nonparametric Kaplan-Meier Estimator of the Cumulative Incidence Function in Competiting Risks

Download PDF (606.4 KB) PP. 1 - 13 Pub. Date: March 9, 2018

DOI: 10.22606/jas.2018.31001

Author(s)

Didier Alain Njamen Njomen^*
Department of Mathematics and Computer Science, Faculty of Science, University of Maroua, Cameroon

Abstract

In this paper, inspired by the estimator of the cumulated specific incidence proposed by Marubini and Vasecchi [23], we obtain the Kaplan-Meier estimator of the survival function of all causes of death combined by summing the estimator of fj(t) (j 2 {1, . . . ,m}) obtained by plug-in. We establish that the Kaplan-Meier estimator of the survival function overestimates the cumulative incidence in the presence of competitive events. By making the product of all the contributions of the studied system, we establish the likelihood function of the specific risk function for the competitive risk model. Finally, under the assumptions of Dinse and Larson [13], and using the delta-method, we establish the variance of the cumulative incidence function in competiting risks.

Keywords

Survival analysis; competiting risks; function of cumulative incidence; Kaplan-Meier estimators; risk function of specific cause; likelihood function; delta-method.

MSC 2000: 62Nxx, 62NO1, 62-07, 62Gxx, 62NO2, 62G05.62Hxx, 62J10

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