The semi-parametric proportional hazards model is widely adopted in randomized clinical trials with time-to-event outcomes, and the log-rank test is frequently used to detect a potential treatment effect. Immuno-oncology therapies pose unique challenges to the design of a trial as the treatment effect may be delayed, which violates the proportional hazards assumption, and the log-rank test has been shown to markedly lose power under the non-proportional hazards setting. A novel design and analysis approach for immuno-oncology trials is proposed through a piecewise treatment effect function, which is capable of detecting a potentially delayed treatment effect. The number of events required for the trial will be determined to ensure sufficient power for both the overall log-rank test without a delayed effect and the test beyond the delayed period when such a delay exists. The existence of a treatment delay is determined by a likelihood ratio test with resampling. Numerical results show that the proposed design adequately controls the Type I error rate, has a minimal loss in power under the proportional hazards setting and is markedly more powerful than the log-rank test with a delayed treatment effect.