Testing the hypothesis of increasing hazard ratio in two samples

Tests designed to detect increasing hazard ratio against the proportional hazards hypothesis are generally consistent for other alternatives also. This article provides a test of the null hypothesis of increasing hazard ratio. The test is based on the separation between an empirical version of the relative trend function and its greatest convex minorant. The proportional hazards model, the least favorable null model for large samples, is used to produce simulation based cutoffs. A simulation study shows reasonable performance of the proposed test in small samples. The analytical test, together with a graphical version, is illustrated through two real life examples.