Approximate tests for the equality of two cumulative incidence functions of a competing risk

ABSTRACT

In the context of a competing risks set-up, we discuss different inference procedures for testing equality of two cumulative incidence functions, where the data may be subject to independent right-censoring or left-truncation. To this end, we compare two-sample Kolmogorov–Smirnov- and Cramér–von Mises-type test statistics. Since, in general, their corresponding asymptotic limit distributions depend on unknown quantities, we utilize wild bootstrap resampling as well as approximation techniques to construct adequate test decisions. Here, the latter procedures are motivated from tests for heteroscedastic factorial designs but have not yet been proposed in the survival context. A simulation study shows the performance of all considered tests under various settings and finally a real data example about bloodstream infection during neutropenia is used to illustrate their application.

KEYWORDS:

• Aalen–Johansen estimator
• approximation techniques
• competing risk
• cumulative incidence function
• wild bootstrap

Acknowledgments

The authors like to thank Arthur Allignol, Jan Beyersmann, Tobias Bluhmki and Edgar Brunner for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Moreover, both authors would like to thank the support received by the Heinrich-Heine University Düsseldorf SFF [grant number F-2012/375-12].