Conditional tests in a competing risks model

Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors. The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests. In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data). The resulting conditional tests are initially developed for the case of k = 2 and are then extended to k > 2 by performing a sequence of two sample tests and by combining several risks into one. A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power. A real life example is also discussed to show how to implement such conditional tests.