AbstractChimeric antigen receptor T-cell (CAR-T) therapy is an exciting development in the field of cancer immunology and has received a lot of interest in recent years. Many time-to-event (TTE) endpoints related to relapse, disease progression, and remission are analyzed in CAR-T studies to assess treatment efficacy. Definitions of these TTE endpoints are not always consistent, even for the same outcomes (e.g., progression-free survival), which often stems from analysis choices regarding which events to consider as part of the composite endpoint, censoring or competing risk in the analysis. Subsequent therapies such as hematopoietic stem cell transplantation are common but are not treated the same in different studies. Standard survival analysis methods are commonly applied to TTE analyses but often without full consideration of the assumptions inherent in the chosen analysis. We highlight two important issues of TTE analysis that arise in CAR-T studies, as well as in other settings in oncology: the handling of competing risks and assessing the association between a time-varying (post-infusion) exposure and the TTE outcome. We review existing analytical methods, including the cumulative incidence function and regression models for analysis of competing risks, and landmark and time-varying covariate analysis for analysis of post-infusion exposures. We clarify the scientific questions that the different analytical approaches address and illustrate how the application of an inappropriate method could lead to different results using data from multiple published CAR-T studies. Codes for implementing these methods in standard statistical software are provided.