Competing risks models: Problems of modelling and of identification

Abstract

In this chapter we consider problems met in modelling data of the following type. For a given individual, we observe the age at the time of death, say T, and the cause of the death, say A, among a finite set of possible causes, say E = {1, 2, ... , p}. The finite character of A may raise difficulties in applications where, for instance, the number of causes may increase with time without a priori given limits; this is the case of mutating viruses for instance. In such situations, A might be conceptually infinite; this feature would call for modification of the models to be presented. For statistical purposes, models typically consider a finite number of precisely defined causes along with a “residual” cause that gathers all other possible causes; this residual cause is often treated as a censoring state.