The probability-of-being-in-response (PBR) curve is a graphical method that combines two time-to-event endpoints, namely time from study start to first response and time from first response to subsequent failure considering all patients of a study. We generalize the logrank-test to a test that compares PBR curves. We focus on the global null hypothesis of no difference between the multistate stochastic processes underlying the two curves. The test is designed in such a way that it has high power when the PBR is consistently higher for one of the two groups at all times. Simulations and the application to clinical trial data show that the proposed tests are useful additions to the visual comparison of PBR curves.