The novel mechanism of action of immunotherapy agents, in treatment of various types of cancer, poses unique challenges during the designing of clinical trials. It is important to account for possibility of a delayed treatment effect and adjust sample size accordingly. This paper provides an analytical approach for computing sample size in the presence of a delayed effect using a piece-wise proportional hazards model. Failing to account for an anticipated treatment delay may result in considerable loss in power. The overall hazard ratio (HR), which now represents the average HR across the entire treatment period, can remain a meaningful measure of average benefit to patients in the trial. We show that, special consideration needs to be given for the designing of interim analyses related to futility, so as not to increase the probability of incorrectly stopping an effective agent. It is shown that the weighted log-rank test, using the Fleming-Harrington class of weights, can be used as supportive analysis to better reflect the impact of a delayed effect and possible long-term benefit in a subset of the overall population.