Effective comparison of two potentially crossing hazard rate curves

Abstract

In survival data analysis, comparison of two hazard rate curves is critically important for evaluating a treatment effect. In many applications, the two hazard curves could potentially cross each other, violating the proportional hazards assumption in the Cox's model. In such cases, the traditional tests like the log-rank test and the Peto-Peto test that were developed based on that assumption would be ineffective. There have been some discussions in the literature on comparison of two potentially crossing hazard curves, based on either parametric modeling or nonparametric testing approaches. However, the assumed models of the existing parametric methods are often difficult to justify in practice. On the other hand, the existing nonparametric tests are usually based on the maximization with respect to an unknown crossing point, leading to complex null distributions for the corresponding test statistics. We suggest a novel method in this paper for comparing two hazard curves based on a nonparametric testing procedure. Its test statistic avoids the maximization mentioned above and consequently has the desirable asymptotic normality property under some regularity conditions. We show that the new method is effective for comparing two potentially crossing hazard curves.