In study designs for randomized clinical trials with a survival endpoint, the log-rank test is commonly used and the treatment effect is hypothesized with a proportional hazards alternative. Recently, treatment effects frequently seen in successful cancer immunotherapy trials have been manifested through a delayed effect pattern with a lag time, raising challenges to the use of conventional study design hypotheses. In particular, when a trial with interim analyses is designed using a group sequential method, the expected treatment effect from a log-rank test statistic varies across analysis times and differs from the parameter specified in the alternative hypothesis. In this paper, we present statistical analytical work that formulates a design including interim analyses with a survival endpoint under a delayed treatment effect alternative. Closed-form solutions are provided for calculating power and sample size over varying study/follow-up times for the group sequential, delayed treatment effect design. The analytical work is also presented graphically and a simulation is conducted for validation.