Group sequential tests for treatment effect on survival and cumulative incidence at a fixed time point

Medical research frequently involves comparing an event time of interest between treatment groups. Rather than comparing the entire survival or cumulative incidence curves, it is sometimes preferable to evaluate these probabilities at a fixed point in time. Performing a covariate adjusted analysis can improve efficiency, even in randomized clinical trials, but no currently available group sequential test for fixed point analysis provides this adjustment. This paper introduces covariate adjusted group sequential pointwise comparisons of survival and cumulative incidence probabilities. Their test statistics have an asymptotic distribution with independent increments, permitting use of common stopping boundary specification methods. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylactic treatment for adverse outcomes following blood and marrow transplantation. A simulation study demonstrates that these tests maintain the type I error rate and power at nominal levels under a variety of settings involving influential covariates.