The Annals of Statistics

A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk

Robert J. Gray

Full-text: Open access


In this paper, for right censored competing risks data, a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups. The tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest. Asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory. It is proposed that weight functions very similar to those for the $G^p$ tests from ordinary survival analysis be used. Simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples.

Article information

Ann. Statist., Volume 16, Number 3 (1988), 1141-1154.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G10: Hypothesis testing
Secondary: 62E20: Asymptotic distribution theory

Censored data counting processes martingales $G^\rho$ tests


Gray, Robert J. A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk. Ann. Statist. 16 (1988), no. 3, 1141--1154. doi:10.1214/aos/1176350951.

Export citation