Implementation of an alternative method for assessing competing risks: restricted mean time lost

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 all have some limitations related to model assumptions and clinical interpretation. Therefore, we introduce restricted mean time lost (RMTL) as an alternative that is easy to interpret in a competing risks framework. We propose a hypothetical test and sample size estimator based on the difference in RMTL (RMTLd). The simulation results show that the RMTLd test has robust statistical performance (both type I error and power). Meanwhile, the RMTLd-based sample size can approximately achieve the predefined power level. The results of two 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 when analyzing competing risks data and that the RMTLd even be regarded as the primary outcome when the proportional hazard assumption fails.