Shared frailty models

Abstract

The shared frailty model is a specific kind of the common risks model described in Section 3.1.2. The frailty is the term that describes the common risks, acting as a factor on the hazard function. The approach makes sense both for parallel data and recurrent events data. In this chapter, only parallel data are considered. The results are presented in terms of individuals, which have the same risk in some groups. Recurrent events data will be separately considered in Chapter 9. The shared frailty model is relevant to lifetimes of several individuals, similar organs and repeated measurements. It is not generally relevant for the case of different events. It is a mixture model, because in most cases the common risks are assumed random. The mixture term is the frailty and for this the notation Y will be used. The model assumes that all time observations are independent given the values of the frailties. In other words, it is a conditional independence model. The value of Y is constant over time and common to the individuals in the group and thus is responsible for creating dependence. This is the reason for the word shared, although it would be more correct to call the models of this chapter constant shared frailty models. The interpretation of this model is that the between-groups variability (the random variation in Y) leads to different risks for the groups, which then show up as dependence within groups. The approach is a multivariate version of the mixture calculations of Sections 2.2.7 and 2.4.6.