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

TLDR

The study introduces a class of tests for comparing the cumulative incidence of a specific failure type across groups in right‑censored competing risks data. The tests compare weighted averages of the subdistribution hazard, with asymptotic properties derived from counting processes and martingale central limit theory, using weight functions akin to the G^p tests from survival analysis. Simulation studies demonstrate that the asymptotic distributions provide adequate approximations for moderate sample sizes.

Abstract

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.