Implementation of an Alternative Method for Assessing Competing Risks: Restricted Mean Time Lost

In clinical and epidemiologic studies, hazard ratios are often applied to compare treatment effects between 2 groups for survival data. For competing-risks data, the corresponding quantities of interest are cause-specific hazard ratios and subdistribution hazard ratios. However, they both have some limitations related to model assumptions and clinical interpretation. Therefore, we recommend restricted mean time lost (RMTL) as an alternative measure that is easy to interpret in a competing-risks framework. Based on the difference in RMTL (RMTLd), we propose a new estimator, hypothetical test, and sample-size formula. Simulation results show that estimation of the RMTLd is accurate and that the RMTLd test has robust statistical performance (both type I error and statistical power). The results of 3 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 along with the hazard ratio in analyses of competing-risks data and that the RMTLd even be regarded as the primary outcome when the proportional hazards assumption fails.