Competing risks models

Abstract

The term competing risks refers to cause of death models. Competing risks have been introduced and illustrated as a multi-state model in Figure 1.7 and discussed previously, in Sections 1.10, 3.3.9, and Chapter 5; but such data present special challenges, and therefore are considered separately in this chapter. It differs from the rest of this book in that only one event is possible for each individual, and in that sense, the concept of dependence seems irrelevant. However, two problems stand out as particularly important for competing risks data, the possibility of classification error and, more important, the desire to study the effect of modifying the hazards for some causes of death. Therefore, dependence is the key problem for such data. We would like to discuss aspects where dependence is important, but it is impossible to estimate the degree of dependence. In fact, it is impossible even to give a specific interpretation of dependence. The problem is caused by competing risks not being a truly multivariate survival problem. This has been discussed for centuries, since Bernoulli considered what the eradication of smallpox would imply for the mean lifetime.