ABSTRACT
A frailty model is a random effects model dedicated to survival data. This means that there is a model describing a basic random variation and on top of this there is an additional random variation (which is the one that the term frailty refers to). This random effect can be used for univariate (independent) data in order to obtain a more flexible model, or specifically describe overdispersion in relation to the basic random variation. It is, however, more interesting to use the random effect in the multivariate case as a means to model dependence between the observations. Four cases of multivariate survival data stand out as particularly relevant for the use of a frailty model: first, the case of related individuals, such as twins, family members or matched pairs; second, the case of similar organs (or other kinds of components) in an individual, for example, right and left eye or a set of teeth; third, the case of recurrent events, where multiple occurrences of similar events are happening for an individual, for example, epilectic seizures, or hypoglycaemic episodes in diabetes; fourth, times that come out from a designed experiment, where a single individual goes through multiple treatments, where in each case, the time to some event is recorded. The model will be introduced as covering survival times for one or more related individuals, but it can also be used in the other cases mentioned, as will be demonstrated later.
