Logrank/hazard ratio (HR) test/estimation approach has been routinely used in almost all cancer clinical trials with time-to-event outcomes. Although the logrank test is an asymptotically valid nonparametric test, it is not the most powerful test when the pattern of the difference is non-proportional hazards (PH). Also, under the violation of PH, interpretation of the HR is not apparent. For immunotherapy trials, we often see a delayed difference pattern, which suggests the conventional logrank/HR approach is not appropriate for testing equality nor estimating the magnitude of the treatment effect. RMST-based analysis is a good alternative since it can provide a robust and interpretable summary of the treatment effect. We propose a RMST-based approach particularly when a delayed difference pattern can be expected. The proposed approach lets the data choose the time point where two survival curves start separate, and quantifies a long-term treatment effect using difference in area under the survival curve. Simulation studies show how effectively the proposed method can detect the treatment difference, compared to the logrank test, MaxCombo test, standard RMST-based tests, and so on.