Background: In studies of all-cause mortality, a one-to-one relation connects the hazard with the survival and as a consequence the regression models which focus on the hazard, such as the proportional hazards model, immediately dictate how the covariates relate to the survival function, as well. However, these two concepts and their one-to-one relation are totally different in the context of competing risks, where the terms of cause-specific hazard and cumulative incidence function appear. Objective: The aim of the present work was to present two of the most popular methods (cause-specific hazard model and Fine & Gray model) through an application on cardiovascular disease epidemiology (CVD), as well as, to narratively review more recent publications, based on either the frequentist, or the Bayesian approach to inference. Methods: A narrative review of the most widely used methods in the competing risks setting was conducted, extended to more recent publications. For the application, our interest lied in modeling the risk of Coronary Heart Disease in the presence of vascular stroke, by using the cause-specific hazard and the Fine & Gray models, two of most commonly encountered approaches. Results-Conclusions: After the implementation of these two approaches in the context of competing risks in CVD epidemiology, it is noted that while the use of the Fine & Gray model includes information about the existence of a competing risk, the interpretation of the results is not as easy as in the case of the cause-specific risk Cox model.
Maximum Likelihood Estimation for Cox Proportional Hazards Model with a Change Hyperplane
