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

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, left-truncation or even -filtering. 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.