Cancer immunotherapies provides new hopes for cancer patients such as melanoma and lung cancer. Given the particularly different mechanism of action for immunotherapy comparing to chemotherapy, the way to assess the drug effect is evolving. The drug effect may display a 'delayed' phenomenon, i.e. observed after patents receiving the drug for a while. In medical community, several approaches are proposed for this consideration such as immune-related response criteria (irRC) and immune-related RECIST. In addition, immune response data collected after patients receiving the drug may correlate to the clinical outcomes, and may also correlate to other biomarkers such as genetic markers. As statisticians, how can we take consideration of these observations in statistical modeling and hypothesis testing?