  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
