Nonparametric hypothesis testing

Abstract

The log-rank test is arguably the most widely used test in survival analysis. In this brief Chapter, we explain the idea of the log-rank test and how it translates to competing risks. The key issue is that the log-rank test compares hazards and may consequently be used to compare cause-specific hazards, too. As we have seen earlier, differences between cause-specific hazards do not translate into differences of the cumulative event probabilities in a straightforward manner. Therefore, cumulative incidence functions are often compared by a log-rank-type test for the subdistribution hazard rather than for the cause-specific hazards. As we show below, we may settle for a brief Chapter, because these tests have already been computed as a byproduct of the Cox-type models in Chapter 5.