Generalizations and applications of frailty models for survival and event data.

A variety of survival models with both discrete and continuously distributed frailty is considered within a framework that involves the specification of three sub-models. An intensity sub-model specifies how the intensity is related to values of covariates and frailty; a measurement sub-model specifies how fallible measures of frailty are related to it; and an exposure sub-model specifies how frailty is distributed within the population. The models include those in which frailty is due to omitted covariates and those where it represents a covariate that has been measured subject to error. Multivariate frailty is also considered, with particular emphasis on models suitable for application to genetically related individuals, notably twins. A numerical example illustrates the use of a model with multivariate frailty for data on repeated exercise times.