Applying the Cox proportional hazard regression model to competing risks

In the presence of dependent competing risks in survival analysis, the Cox proportional hazard model can be utilised to examine the covariate effects on the cause-specific hazard function for each type of failure. The use of the Cox model was proposed by Lunn and McNeil (Biometrics, 1995). Their method requires data augmentation. With k failure types, the data would be duplicated k times, one record for each failure type. Either a stratified or an unstratified analysis could be used, depending on whether the assumption of proportional hazard holds. If the proportional hazard assumption does not hold across the causes, the stratified analysis should be used, which is equivalent of fitting separate model for each failure type. The unstratified analysis assumes a constant hazard ratio between failure types and this could be fitted by including an indicator variable as a covariate. We will show how both approaches could be fitted on augmented data using stcox. In addition to the parameter estimates and their standard errors, the program has an option to produce cumulative incidences with pointwise confidence interval.