Comptes Rendus
no. 5
Statistics
A U-statistic test in competing risk models
[Une U-statistique pour les modèles à risques compétitifs]

Présenté par : Paul Deheuvels

Nicolas Molinari1
1 Laboratoire de biostatistique, institut universitaire de recherche clinique, 641, avenue Gaston-Giraud, 34093 Montpellier, France
Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 317-322.

Considérons la situation où un individu est soumis à différents risques compétitifs de décès et à un processus de censure indépendant. Une approche, basée sur une U-statistique, permet de tester l'hypothèse d'égalité de deux risques compétitifs. Sous des hypothèses d'indépendence, nous obtenons la distribution asymptotique de la statistique de test.

We consider a situation in which systems are subject to failure from competing risks or could be censored from an independent censoring process. A procedure, based on a U-statistic, is proposed for testing the equality of two failure rates in the competing risks set. Under independence assumptions, the asymptotic distribution of the statistic is given and used to construct the test.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.07.016
Nicolas Molinari 1

1 Laboratoire de biostatistique, institut universitaire de recherche clinique, 641, avenue Gaston-Giraud, 34093 Montpellier, France 
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Nicolas Molinari. A U-statistic test in competing risk models. Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 317-322. doi : 10.1016/j.crma.2005.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.07.016/

[1] E.A.A. Aly; S.C. Kochar; I.W. McKeague Some tests for comparing cumulative incidence functions and cause-specific hazard rates, J. Amer. Statist. Assoc., Volume 89 (1994), pp. 994-999

[2] G. Aras; J.V. Deshpande Statistical analysis of dependent competing risks, Statistics and Decisions, Volume 10 (1992), pp. 323-336

[3] I. Bagai; J.V. Deshpande; S.C. Kochar Distribution free tests for stochastic ordering in the competing risks model, Biometrika, Volume 76 (1989), pp. 776-781

[4] C.L. Chiang Introduction to Stochastic Processes in Biostatistics, Wiley, New York, NY, 1968

[5] M.J. Crowder Classical Competing Risks, CRC Press, Boca Raton, FL, 2001

[6] W. Hoeffding A class of statistics with asymptotically normal distribution, Ann. Math. Statist., Volume 19 (1948), pp. 293-325

[7] N. Keyfitz; S.H. Preston; R. Schoen Inferring probabilities from rates: extension to multiple decrements, Skandinavisk Aktuarietidskrift (1972), pp. 1-13

[8] P. Yip; K.F. Lam A class of non-parametric tests for the equality of failure rates in a competing risks model, Commun. Statist. – Theory and Methods, Volume 21 (1992), pp. 2541-2556

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