On testing the proportionality of two cumulative incidence functions in a competing risks setup

Abstract

A large sample test of proportionality of two cumulative incidence functions is developed for randomly right censored competing risks data without assuming that the K ≥ 2 risks are independent. The test is tailored to detecting monotonicity of the ratio of the two cumulative incidence functions and the test statistic is proved to be asymptotically normally distributed. In addition, it is shown that the proposed test can be readily adapted to test whether the censoring random variable and observable survival time have proportional hazards. The procedures are illustrated through application to two data sets well known in the survival analysis literature.

Keywords:

• Aalen–Johansen estimator
• Absolute cause-specific risk
• Asymptotic normality
• Crude incidence curve
• Koziol–Green model
• Random right-censoring
• Retro-hazard
• Total positivity of order 2

Acknowledgement

The authors thank CREST-ENSAI and the University of Northern Iowa for the necessary financial support. They also thank Professor Michael Akritas and a referee for their helpful comments.