A class of tests for the equality of k cause-specific hazard rates in a competing risks model

Abstract

A class of asymptotically distribution-free tests for the equality of the k risks in a competing risks model is considered. The tests can be derived by martingale theory or by a marginal likelihood approach. When the risks are dependent, the quantities to be compared would be the cause-specific hazard rates or equivalently the pseudosurvivor functions related to the cause-specific hazard rates. This class of tests allows one to compare k risks simultaneously for k > 2, is able to handle possibly right-censored data and is extremely simple to apply. Choices of the optimal weight functions leading to the locally most powerful rank tests for a general class of semiparametric alternative hypotheses are discussed. The performances of the tests are studied by simulation under various alternative hypotheses.