A challenge arising in cancer immunotherapy trial design is the presence of a delayed treatment effect wherein the proportional hazard assumption is no longer holds true. As a result, a traditional survival trial design based on the standard log-rank test which ignores the delayed treatment effect will lead to substantial loss of statistical power.
Recently, Xu et al. proposed using a piece-wise weighted log-rank test to incorporate the delayed treatment effect into consideration of the trial design. However, because their sample size formula was derived under a sequence of local alternative hypotheses it results in an underestimated sample size when the hazard ratio is small for a balanced trial design and inaccurate sample size estimation for an unbalanced design. In this article, we derived a new sample size formula under a fixed alternative hypothesis. Simulation results show that the new formula provides accurate sample size estimation for both balanced and unbalanced designs.