Z_max test for delayed effect in immuno-oncology clinical trials

ABSTRACT

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.

KEYWORDS:

• Z_max test
• log-rank test
• weighted log-rank test
• Fleming-Harrington
• delayed effect
• immuno-oncology
• clinical trials

Acknowledgments

The paper is substantially improved thanks to the helpful comments of an associate editor and the referees. Research has been supported by National Science Foundation grant DMS 1812258.