Simulation shows undesirable results for competing risks analysis with time-dependent covariates for clinical outcomes

Inga Poguntke, Martin Schumacher, Jan Beyersmann, Martin Wolkewitz

We evaluate three methods for competing risks analysis with time-dependent covariates in comparison with the corresponding methods with time-independent covariates. We used cause-specific hazard analysis and two summary approaches for in-hospital death: logistic regression and regression of the subdistribution hazard. We analysed real hospital data (n=1864) and considered pneumonia on admission / hospital-acquired pneumonia as time-independent / time-dependent covariates for the competing events 'discharge alive' and 'in-hospital death'. Several simulation studies with time-constant hazards were conducted. All approaches capture the effect of time-independent covariates, whereas the approaches perform differently with time-dependent covariates. The subdistribution approach for time-dependent covariates detected effects in a simulated no-effects setting and provided counter-intuitive effects in other settings. The extension of the Fine and Gray model to time-dependent covariates is in general not a helpful synthesis of the cause-specific hazards. Cause-specific hazard analysis and, for uncensored data, the odds ratio are capable of handling competing risks data with time-dependent covariates but the use of the subdistribution approach should be neglected until the problems can be resolved. For general right-censored data, cause-specific hazard analysis is the method of choice.