Frailty distributions

Different distributions have been proposed for the frailty term. In Chapter 2 the gamma distribution was introduced. In this chapter we discuss different frailty distributions that are proposed in the literature. Although the discussion in this chapter is rather technical (most of the results appeared in methodological journals), it is important to collect what is available in a detailed way. Indeed, in practice mainly the gamma distribution and the lognormal distribution are used to model the frailty term and most of the software limits the choice of the frailty distribution to these cases. But the right choice of the frailty distribution is of crucial importance to arrive at a good description of the dependence structure present in the data. Therefore, the choice of the frailty distribution is even more important as the choice of the distribution of the random effect(s) in mixed models since, in frailty models, the dependence between correlated observations changes over time and the frailty distribution dictates how the dependence changes. Few results are available on comparing models with different frailty distributions; more research is needed in this area.