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 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. The R code (crRMTL) is publicly available from Github (https://github.com/chenzgz/crRMTL.1). Keywords: survival analysis, competing risks, hazard ratio, restricted mean time lost, sample size, hypothesis test