In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time. The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on the cRMST can be established by incorporating time-dependent covariates and covariates with time-varying effects. We analysed data from a study of primary biliary cirrhosis (PBC) to illustrate the use of the dynamic RMST model. The predictive performance was evaluated using the C-index and the prediction error. The proposed dynamic RMST model, which can explore the dynamic effects of prognostic factors on survival time, has better predictive performance than the RMST model. Three PBC patient examples were used to illustrate how the predicted cRMST changed at different prediction times during follow-up. The use of the dynamic RMST model based on the cRMST allows for optimization of evidence-based decision-making by updating personalized dynamic life expectancy for patients.

In clinical and epidemiological studies, hazard ratios are often applied to compare treatment effects between two groups for survival data. For competing risks data, the corresponding quantities of interest are cause-specific hazard ratios (cHRs) and subdistribution hazard ratios (sHRs). However, they both have some limitations related to model assumptions and clinical interpretation. Therefore, we recommend restricted mean time lost (RMTL) as an alternative that is easy to interpret in a competing risks framework. Based on the difference in restricted mean time lost (RMTLd), we propose a new estimator, hypothetical test and sample size formula. The simulation results show that the estimation of the RMTLd is accurate and that the RMTLd test has robust statistical performance (both type I error and power). The results of three example analyses also verify the performance of the RMTLd test. From the perspectives of clinical interpretation, application conditions and statistical performance, we recommend that the RMTLd be reported with the HR in the analysis of competing risks data and that the RMTLd even be regarded as the primary outcome when the proportional hazard assumption fails.

In clinical or epidemiological follow-up studies, methods based on time scale indicators such as the restricted mean survival time (RMST) have been developed to some extent. Compared with traditional hazard rate indicator system methods, the RMST is easier to interpret and does not require the proportional hazard assumption. To date, regression models based on the RMST are indirect or direct models of the RMST and baseline covariates. However, time-dependent covariates are becoming increasingly common in follow-up studies. Based on the inverse probability of censoring weighting (IPCW) method, we developed a regression model of the RMST and time-dependent covariates. Through Monte Carlo simulation, we verified the estimation performance of the regression parameters of the proposed model. Compared with the time-dependent Cox model and the fixed (baseline) covariate RMST model, the time-dependent RMST model has a better prediction ability. Finally, an example of heart transplantation was used to verify the above conclusions. K E Y W O R D Sinverse probability of censoring weighting, restricted mean survival time, survival analysis, time-dependent covariates 1

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.