  Background: Under competing risks, the commonly used sub-distribution hazard
ratio (SHR) is not easy to interpret clinically and is valid only under the
proportional sub-distribution hazard (SDH) assumption. This paper introduces an
alternative statistical measure: the restricted mean time lost (RMTL). Methods:
First, the definition and estimation methods of the measures are introduced.
Second, based on the differences in RMTLs, a basic difference test (Diff) and a
supremum difference test (sDiff) are constructed. Then, the corresponding
sample size estimation method is proposed. The statistical properties of the
methods and the estimated sample size are evaluated using Monte Carlo
simulations, and these methods are also applied to two real examples. Results:
The simulation results show that sDiff performs well and has relatively high
test efficiency in most situations. Regarding sample size calculation, sDiff
exhibits good performance in various situations. The methods are illustrated
using two examples. Conclusions: RMTL can meaningfully summarize treatment
effects for clinical decision making, which can then be reported with the SDH
ratio for competing risks data. The proposed sDiff test and the two calculated
sample size formulas have wide applicability and can be considered in real data
analysis and trial design.
