Regression in the Presence of Competing Risks: A Simulation Study on Covariate and Competing Risk Correlations

In the analysis of survival data, competing risks demand consideration of non-standard methods, since standard methods do not account for the presence of any competing events. This study investigates how the correlation between a treatment covariate and a competing event influences the hazard ratio estimates from the cause-specific Cox proportional hazards model and the Fine-Gray subdistribution hazards model. Simulated survival data with independent event times is used, where the size and direction of the correlation between treatment and the competing event are varied. The effect of the correlation is considered under varying censoring proportions, sample sizes of the primary event, and hazard specifications. The results show that correlations of ±0.2 and ±0.4 lead to noticeable differences in estimates (compared to zero correlation) from the Fine-Gray model and the cause-specific Cox model for the competing event, while the cause-specific primary event model remains stable. The findings emphasise the need to assess any potential associations between covariates and competing events when considering survival analysis regression models.