Time-varying effect in the competing risks based on restricted mean time lost

Abstract: Patients with breast cancer tend to die from other diseases, so for studies that focus on breast cancer, a competing risks model is more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor. To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale. Through Monte Carlo simulation, we validated the dynamic effects estimated by the proposed regression having low bias and a coverage rate of around 95%. Applying this model to an elderly early-stage breast cancer cohort, we found that most factors had different patterns of dynamic effects, revealing meaningful physiological mechanisms underlying diseases. Moreover, from the perspective of prediction, the mean C-index in external validation reached 0.78. Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist.