• Additive risk model;
  • Competing risks;
  • Confidence bands;
  • Confidence intervals;
  • Martingale

Summary. In the context of competing risks, the cumulative incidence function is often used to summarize the cause-specific failure-time data. As an alternative to the proportional hazards model, the additive risk model is used to investigate covariate effects by specifying that the subject-specific hazard function is the sum of a baseline hazard function and a regression function of covariates. Based on such a formulation, we present an approach to constructing simultaneous confidence intervals for the cause-specific cumulative incidence function of patients with given risk factors. A melanoma data set is used for the purpose of illustration.