SOME TESTS FOR COMPARING CUMULATIVE INCIDENCE FUNCTIONS AND CAUSE-SPECIFIC HAZARD RATES

We consider the competing risks problem with the available data in the form of times and causes of failure. In many practical situations (e.g., in reliability testing) it is important to know whether two risks are equal or whether one is ''more serious'' than the other. We propose some distribution-free tests for comparing cumulative incidence functions and cause-specific hazard rates against ordered alternatives without making any assumptions on the nature of dependence between the risks. Both the censored and the uncensored cases are studied. The performance of the proposed tests is assessed in a simulation study. As an illustration, we compare the risks of two types of cancer mortality (thymic lymphoma and reticulum cell carcinoma) in a strain of laboratory mice.