Group sequential monitoring based on the maximum of weighted log-rank statistics with the Fleming-Harrington class of weights in oncology clinical trials.

Clinical trials in oncology often involve the statistical analysis of time-to-event data such as progression-free survival or overall survival to determine the benefit of a treatment or therapy. The log-rank test is commonly used to compare time-to-event data from two groups. The log-rank test is especially powerful when the two groups have proportional hazards. However, survival curves encountered in oncology studies that differ from one another do not always differ by having proportional hazards; in such instances, the log-rank test loses power, and the survival curves are said to have "non-proportional hazards". This non-proportional hazards situation occurs for immunotherapies in oncology; immunotherapies often have a delayed treatment effect when compared to chemotherapy or radiation therapy. To correctly identify and deliver efficacious treatments to patients, it is important in oncology studies to have available a statistical test that can detect the difference in survival curves even in a non-proportional hazards situation such as one caused by delayed treatment effect. An attempt to address this need was the "max-combo" test, which was originally described only for a single analysis timepoint; this article generalizes that test to preserve type I error when there are one or more interim analyses, enabling efficacious treatments to be identified and made available to patients more rapidly.