Combined tests based on restricted mean time lost for competing risks data

TL;DR

This paper introduces the restricted mean time lost (RMTL) as an alternative measure for competing risks data, develops combined tests based on RMTL and sub-distribution hazard ratios, and demonstrates their robustness and practical utility through simulations and real data applications.

Contribution

The paper proposes RMTL as a clinically interpretable alternative to hazard ratios and develops combined tests that are robust and effective for competing risks analysis.

Findings

Combined tests maintain nominal type I error levels.

All tests exhibit acceptable power across scenarios.

RMTL effectively summarizes treatment effects for clinical decisions.

Abstract

Competing risks data are common in medical studies, and the sub-distribution hazard (SDH) ratio is considered an appropriate measure. However, because the limitations of hazard itself are not easy to interpret clinically and because the SDH ratio is valid only under the proportional SDH assumption, this article introduced an alternative index under competing risks, named restricted mean time lost (RMTL). Several test procedures were also constructed based on RMTL. First, we introduced the definition and estimation of RMTL based on Aalen-Johansen cumulative incidence functions. Then, we considered several combined tests based on the SDH and the RMTL difference (RMTLd). The statistical properties of the methods are evaluated using simulations and are applied to two examples. The type I errors of combined tests are close to the nominal level. All combined tests show acceptable power in all situations. In conclusion, RMTL can meaningfully summarize treatment effects for clinical decision making, and three combined tests have robust power under various conditions, which can be considered for statistical inference in real data analysis.