The topic of cancer immunology has seen a surge of attention in recent years because of the promising potential of chimeric antigen receptor T-cell (CAR-T) treatment. To evaluate the effectiveness of CAR-T therapy, researchers examine a wide variety of time-to-event (TTE) endpoints, including recurrence, disease progression, and remission. Unfortunately, even for the same outcomes (like progression-free survival), there is inconsistency in the definitions of TTE endpoints. This is usually due to analysis choices like selecting events to include in the composite endpoint, censoring, or competing risk. While follow-up treatments such as hematopoietic stem cell transplantation are often used, they are rarely consistently evaluated. Typical TTE analyses employ standard survival analysis methods, but this is typically done without fully considering the assumptions inherent in the chosen methodology. Managing competing risks and determining the association between a time-varying (post-infusion) exposure and the TTE outcome are two key concerns of TTE analysis that emerge in CAR-T studies and other cancer contexts. The cumulative incidence function and regression models for comparing risks are discussed, as are landmark and time-varying covariate analyses for examining what happens to a patient after an infusion. Using examples from various CAR-T research, researchers define the specific scientific issues each method seeks to answer and demonstrate how using the wrong technique can alter the outcomes. These methods are implemented in code that can be imported into the most popular statistical packages.