The role of survival functions in competing risks

Competing risks data usually arises in studies in which the failure of an individual may be classified into one of k (k > 1) mutually exclusive causes of failure. When competing risks are present, there are two main differences with classical survival analysis: (i) survival functions are not mainly used to describe cause-specific failures and, (ii) classical estimation techniques may provide biased results. The main goal of this paper is to review, clarify and present the formulation of a competing risks model and the basic nonparametric estimation methods. We show why the use of survival functions in the competing risks framework may mislead the user, and we illustrate the presented methodologies by developing two examples from real data. The methods presented here can be implemented with several statistical packages, including R, SPSS and SAS: we give some highlights on how to perform a competing risks analysis with these software packages.