Background In randomized controlled trials, multiple time-to-event endpoints are commonly used to determine treatment effects. However, choosing an appropriate method to address multiple endpoints, according to different purposes of clinical practice, is a challenge for researchers. Methods We applied single endpoint, composite endpoint and win ratio analysis to chronic myeloid leukemia (CML) data to illustrate the distinctions with different multiple endpoints, including relapse, recovery and death after transplantation. Results Regarding relapse and death, the hazard ratio in single endpoint analysis (HRs) were 1.281 (95% CI: 1.061-1.546) and hazard ratio in composite endpoint analysis (HRc) were 1.286 (95% CI: 1.112-1.486) and 1/WR (win ratio) was 1.292 (95% CI: 1.115-1.497) indicated a similar negative effect for non-prophylaxis patients. However, when considering recovery and death, the corresponding HRs = 1.280 (95% CI: 1.056-1.552) may not be enough to describe the effect on death with nonproportional hazards (p < 0.05), and for the composite endpoint analysis, the HRc = 0.828 (95% CI: 0.740-0.926) cannot quantify and interpret the clinical effect on the composite endpoint with the combination of recovery and death, while the 1/WR = 1.351 (95% CI: 1.207-1.513) showed an unfavourable effect for non-prophylaxis patients Conclusions When dealing with multiple endpoints, single endpoints, researchers may choose single endpoints, composite endpoints and WR analysis due to different clinical applications and purposes. However, both single and composite endpoint analyses are hazard-based measures, and thus, the proportional hazards assumption should be considered. Moreover, composite endpoint analysis should be applied for endpoints with similar clinical meanings but not opposing implications. Win ratio analysis can be considered for different clinical importance of multiple endpoints, but the meaning of 'winner' needs to be specified for desired or undesired endpoints.