Group sequential designs for monitoring survival probabilities

In the present paper we derive the asymptotic joint distribution of the Nelson-Aalen estimators for the cumulative hazard function (or the Kaplan-Meier estimators for the survival function) calculated at different (possibly random) calendar time points of a survival study. This result is used to develop group sequential designs for clinical trials in which patients are enrolled over an extended period and the survival probability at a given failure time point is the parameter of primary interest. The proposed designs allow monitoring the survival probability (or probabilities) at interim looks so that the study can be terminated when there is sufficient evidence for a positive or negative result. A detailed illustration is provided with a problem from the National Wilms Tumor Study Group, which motivated this research.