Generalized nonparametric test procedures for comparing multiple cause-specific hazard rates

In this paper, a generalized nonparametric test procedure for comparing k types of failure in a competing risks model is proposed. The test'procedure is based on the test process defined as a set of weighted integrals of the difference between Aalen-estimated cumulative cause-specific hazards and the average of these estimators. Estimation of the distribution function of the testing process under the null hypothesis is usually the main barrier in developing a test procedure. We introduce a vector of symmetrically inputed processes conditional on the competing risks data and show that the two processes have the same asymptotic distribution under the null hypothesis. This result gives us flexibility in selecting types of statistics and weight functions for various alternatives. Several types of tests including Chi-square type and supremum type for testing the null hypothesis H0 versus various alternative hypotheses are discussed in this paper. With an appro-priate selection of weight function, we also obtain a class of distribution-free tests for competing risks data with k-types of failure.