Comparison of failure probabilities in the presence of competing risks

Typically, differences in the effect of treatment on competing risks are compared by a weighted log-rank test. This test compares the cause specific hazard rates between the groups. Often the test does not agree with the impressions gained from plots of the cumulative incidence functions. Here we discuss several K-sample tests allowing us to directly compare cumulative incidence functions. These include tests based on the weighted integrated difference between the subdistribution hazards or cumulative incidence functions, Kolmogorov-Smirnov type test, and Renyi type test. In addition to unadjusted comparison techniques, tests based on the regression modeling of the cumulative incidence functions are considered. A simulation study is used to compare the various tests and to assess their power against different alternatives. The methods are illustrated using real data examples.