A cancer clinical trial with an immunotherapy often has two special features, which are patients being potentially cured from the cancer and the immunotherapy starting to take clinical effect after a certain delay time. Existing testing methods may be inadequate for immunotherapy clinical trials, because they do not appropriately take the two features into consideration at the same time, hence have low power to detect the true treatment effect. In this talk,we proposed a piece-wise proportional hazards cure rate model with a random delay time to fit data, and a new weighted log-rank test to detect the treatment effect of an immunotherapy over a chemotherapy control. We showed that the proposed weight was nearly optimal under mild conditions. Our simulation study showed a substantial gain of power in the proposed test over the existing tests. We also introduced a sample size calculation formula to design the immunotherapy clinical trials using the proposed weighted log-rank test.