Z_max test for delayed effect in immuno-oncology clinical trials

Delayed separation in survival curves has been observed in immuno-oncology clinical trials. Under this situation, the classic log-rank test may confront high power loss. In this paper, we consider a Z_max test, which is the maximum of the log-rank test and a Fleming-Harrington test. Simulation studies indicate that the Z_max test not only controls the Type I error rate but also maintains good power under different delayed effect models. The asymptotic properties of the Z_max test are also established, which further supports its robustness. We apply the Z_max test to two data sets reported in recent immuno-oncology clinical trials, in which Z_max has exhibited remarkable improvement over the conventional log-rank test.