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In confirmatory clinical trials, survival outcomes are frequently studied and interim analyses for efficacy and/or futility are often desirable. Methods such as the log rank test and Cox regression model are commonly used to compare treatments in this setting. They rely on a proportional hazards (PH) assumption and are subject to type I error rate inflation and loss of power when PH are violated. Such violations may be expected a priori, particularly when the mechanisms of treatments differ such as immunotherapy vs. chemotherapy for treating cancer. We develop group sequential tests for comparing survival curves with covariate adjustment that allow for interim analyses in the presence of non-PH and offer easily interpreted, clinically meaningful summary measures of the treatment effect. The joint distribution of repeatedly computed test statistics converges to the canonical joint distribution with a Markov structure. The asymptotic distribution of the test statistics allows marginal comparisons of survival probabilities at multiple fixed time points and facilitates both critical value specification to maintain type I error control and sample size/power determination. Simulations demonstrate that the achieved type I error rate and power of the proposed tests meet targeted levels and are robust to the PH assumption and covariate influence. The proposed tests are illustrated using a clinical trial dataset from the Blood and Marrow Transplant Clinical Trials Network 1101 trial.
Zhang et al. (Mon,) studied this question.