Group sequential tests for long-term survival comparisons

Sometimes in clinical trials, the hazard rates are anticipated to be nonproportional, resulting in potentially crossing survival curves. In these cases, researchers are usually interested in which treatment has better long-term survival. The log-rank test and the weighted log-rank test may not be appropriate or efficient to use here, because they are sensitive to differences in survival at any time and don't just focus on long-term outcomes. Also in a prospective clinical trial, patients are entered sequentially over calendar time, so that group sequential designs may be considered for ethical, administrative and economic concerns. Here we develop group sequential methods for testing the null hypothesis that the survival curves are identical after a prespecified time point. Several classes of tests are considered, including an integrated difference in survival probabilities after this time point, and linear or quadratic combinations of two component test statistics (pointwise comparisons of survival at the time point and comparisons of hazard rates after the time point). We examine the type I errors, stopping probabilities, and powers of these tests through simulation studies under the null and different alternatives, and we apply them to a real bone marrow transplant clinical trial.