Survival analysis allows to study the time to event under censoring. The event of interest is often death but it can also be any binary variable as e.g. the occurrence of an illness, the relapse of disease, the exit of the hospital,… When an event did not occur for a person, the delay of observation is said censored. A major hypothesis in classical survival analysis is that the time to event and the time to censure are independent. This hypothesis of independence is natural when censure is due to ending follow-up by the researcher (end of a study) or by the patient (volunteer exit independent of the study). When there is a censor for another reason, as e.g. the occurrence of another event which prevents the event of interest from taking place, we speak about competing risks. In this situation, the classical survival analysis is inappropriate and must therefore be adapted. As an example, we will study the problem of cardiac events in renal transplant recipients (RTR) that can die of reasons other than cardiac. A death due to other reasons constitutes a type of event of competing risks since it prevents the observation of the event of interest, namely the death due to a cardiovascular event. Using multivariate Cox regression in 281 RTR, higher log-scaled coronary artery calcifications (CAC) was the only independent predictor of cardiac mortality while multivariate predictors of all cause mortality were a higher log-scaled CAC and log-scaled glycemia. In conclusion, mortality predictors change in presence of competing risks, because of the definition of the mortality of interest.
Henrard, S., & Robert, A. (2008). Competing risks in survival analysis : predictors of cardiovascular events in renal transplant recipients. 16th Annual Meeting of the Belgian Statistical Society, Wépion, Belgium. https://hdl.handle.net/2078.5/216245