Competing-risk models are used to examine the relationship between different risk factors to study different types of failures that may occur in the same population. What would happen to the remaining risks if one or more causes of failure could be eliminated is a question that may be addressed with these models under some conditions. Competing risks are generally evaluated by comparing the predicted time to failure or time to event for the risks being considered.

In this article, the mathematical formulation of the problem is described and statistical methods for estimating competing risk are discussed. Applications of competing risk in the fields of engineering, medicine, economics, and finance are examined with specific examples.