Generalized supremum tests for the equality of cause specific hazard rates

In this paper we propose two new classes of asymptotically distribution-free Renyi-type tests for testing the equality of two risks in a competing risk model with possible censoring. This work extends the work of Aly, Kochar and McKeague [1994, Journal of American Statistical Association, 89, 994-999] and many of the existing tests for this problem belong to these newly proposed classes. The asymptotic properties of the proposed tests are investigated. Simulation studies are done to compare the performance with existing tests. A competing risks data set is analyzed to demonstrate the usefulness of the procedure.