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Biometrika Advance Access published online on August 5, 2007
Biometrika, doi:10.1093/biomet/asm059
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Copyright © 2007 Biometrika Trust

Article

Nonparametric quantile inference with competing–risks data

L. Peng

Department of Biostatistics, Emory University, Atlanta, Georgia 30322, U.S.A.

J. P. Fine

Department of Statistics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.

lpeng{at}sph.emory.edu

fine{at}stat.wisc.edu

Received for publication 1 April 2006. Revision received 1 February 2007.
  Abstract

A conceptually simple quantile inference procedure is proposed for cause-specific failure probabilities with competing risks data. The quantiles are defined using the cumulative incidence function, which is intuitively meaningful in the competing–risks set–up. We establish the uniform consistency and weak convergence of a nonparametric estimator of this quantile function. These results form the theoretical basis for extensions of standard one–sample and two–sample quantile inference for independently censored data. This includes the construction of confidence intervals and bands for the quantile function, and two–sample tests. Simulation studies and a real data example illustrate the practical utility of the methodology.

Key Words: Asymptotic theory • Crude risk function • Dependent censoring • Improper distribution • Nonparametric estimation • Percentile function • Resampling


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