Duration of accrual and follow-up for two-stage clinical trials

Group sequential trials with time to event end points can be complicated to design. Not only are there unlimited choices for the number of events required at each stage, but for each of these choices, there are unlimited combinations of accrual and follow-up at each stage that provide the required events. Methods are presented for determining optimal combinations of accrual and follow-up for two-stage clinical trials with time to event end points. Optimization is based on minimizing the expected total study length as a function of the expected accrual duration or sample size while providing an appropriate overall size and power. Optimal values of expected accrual duration and minimum expected total study length are given assuming an exponential proportional hazards model comparing two treatment groups. The expected total study length can be substantially decreased by including a follow-up period during which accrual is suspended. Conditions that warrant an interim follow-up period are considered, and the gain in efficiency achieved by including an interim follow-up period is quantified. The gain in efficiency should be weighed against the practical difficulties in implementing such designs. An example is given to illustrate the use of these techniques in designing a clinical trial to compare two chemotherapy regimens for lung cancer. Practical considerations of including an interim follow-up period are discussed.