Approximative Tests for the Equality of Two Cumulative Incidence Functions of a Competing Risk

TL;DR

This paper develops and compares approximation-based inference procedures, including bootstrap methods, for testing the equality of two cumulative incidence functions in competing risks data with censoring or truncation, supported by simulations and a real case study.

Contribution

It introduces novel approximation techniques for two-sample tests in competing risks, extending methods from factorial design testing to survival analysis.

Findings

Wild bootstrap improves test accuracy under complex censoring.

Approximation methods perform well compared to bootstrap in simulations.

Application to bloodstream infection data demonstrates practical utility.

Abstract

In the context of the widely used 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 Cramer-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 testing procedures 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.