Applying the Cox proportional hazards regression model to competing risks

In the presence of dependent competing risks in survival analysis, the Cox proportional hazards model can be utilised to examine covariate effects on the cause-specific hazard function for each type of failure. The method proposed by Lunn and McNeil (1995) 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 hazards holds. If the proportional hazards assumption does not hold across the causes, the stratified analysis should be used, which is equivalent to fitting a 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 incidence functions with pointwise confidence limits.