Zhaojin Li,1 Di Liu,2 Yawen Hou,3 Zheng Chen1,4 

1Department of Biostatistics, School of Public Health (Guangdong Provincial Key Laboratory of Tropical Disease Research), Southern Medical University, Guangzhou, People’s Republic of China; 2Department of Oncology, The Second Affiliated Hospital of Xi’an Jiaotong University, Xi’an, People’s Republic of China; 3Department of Statistics and Data Science, School of Economics, Jinan University, Guangzhou, People’s Republic of China; 4State Key Laboratory of Multi-Organ Injury Prevention and Treatment, Guangzhou, People’s Republic of China

Correspondence: Zheng Chen, Email zheng-chen@hotmail.com

Background: In the presence of competing risks, when the baseline risk is unclear, if only the sub-distribution hazard ratio (SHR) is reported in the results, which is related to the cumulative incidence function, the survival disparity of events of interest between groups cannot be clarified. In contrast, the difference in restricted mean time lost (RMTLd), which is the difference in the areas under the cumulative incidence between two groups, can well compensate for the deficiencies of SHR and explain the effects on a time scale, facilitating clinical interpretation and communication.
Methods: The Surveillance, Epidemiology, and End Results (SEER) database was used to collect information on female patients with locally advanced breast cancer diagnosed between 2010 and 2015. The prognostic factors of breast cancer death were evaluated considering competing risk. Univariable and multivariable analyses were conducted to get SHR and RMTLd.
Results: SHR can indicate the direction of prognostic factors, while RMTLd can quantify prognostic effects and provide time-scale interpretation. For instance, in adjuvant radiotherapy, the SHR showed a protective effect, which can be quantified as an average increase of 4.15 months in survival time.
Discussion: In the presence of competing risks, the combined use of absolute measure RMTLd can more intuitively explain the prognostic effect, which is convenient for clinical practice and communication.

Keywords: locally advanced breast cancer, competing risks, restricted mean time lost, sub-distribution hazard ratio