Group sequential methods based on supremum logrank statistics under proportional and nonproportional hazards

Despite the widespread use of Cox regression for modeling treatment effects in clinical trials, in immunotherapy oncology trials and other settings therapeutic benefits are not immediately realized thereby violating the proportional hazards assumption. Weighted logrank tests and the so-called Maxcombo test involving the combination of multiple logrank test statistics have been advocated to increase power for detecting effects in these and other settings where hazards are nonproportional. We describe a testing framework based on supremum logrank statistics created by successively analyzing and excluding early events, or obtained using a moving time window. We then describe how such tests can be conducted in a group sequential trial with interim analyses conducted for potential early stopping of benefit. The crossing boundaries for the interim test statistics are determined using an easy-to-implement Monte Carlo algorithm. Numerical studies illustrate the good frequency properties of the proposed group sequential methods.