Optimal three-stage designs for phase II cancer clinical trials

The objective of a phase II cancer clinical trial is to screen a treatment that can produce a similar or better response rate compared to the current treatment results. This screening is usually carried out in two stages as proposed by Simon. For ineffective treatment, the trial should terminate at the first stage. Ensign et al. extended two-stage optimal designs to three stages; however, they restricted the rejection region in the first stage to be zero response, and the sample size to at least 5. This paper extends Simon's two-stage to a three-stage design without these restrictions, and provides tables for both optimal and minimax designs. One can use the three-stage design to reduce the expected sample size when the treatment is not promising a priori and when the accrual rate is slow. The average reduction in size from a two-stage to three-stage design is 10 per cent.