The use of restricted mean time lost under competing risks data

TL;DR

This paper introduces the restricted mean time lost (RMTL) as an interpretable alternative to the sub-distribution hazard ratio in competing risks data, along with new testing and sample size estimation methods validated through simulations and real data examples.

Contribution

It proposes the RMTL measure for competing risks, along with difference tests and sample size formulas, enhancing interpretability and applicability in clinical studies.

Findings

sDiff test performs well with high efficiency

Sample size estimation methods are robust across scenarios

Methods are validated with simulations and real data examples

Abstract

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.