Two-stage optimal designs with survival endpoint when the follow-up time is restricted

Survival endpoint is frequently used in early phase clinical trials as the primary endpoint to assess the activity of a new treatment. Existing two-stage optimal designs with survival endpoint either over estimate the sample size or compute power outside the alternative hypothesis space.

We propose a new single-arm two-stage optimal design with survival endpoint by using the one-sample log rank test based on exact variance estimates. This proposed design with survival endpoint is analogous to Simon's two-stage design with binary endpoint, having restricted follow-up.

We compare the proposed design with the existing two-stage designs, including the two-stage design with survival endpoint based on the nonparametric Nelson-Aalen estimate, and Simon's two-stage designs with or without interim accrual. The new design always performs better than these competitors with regards to the expected total study length, and requires a smaller expected sample size than Simon's design with interim accrual.

The proposed two-stage minimax and optimal designs with survival endpoint are recommended for use in practice to shorten the study length of clinical trials.