Frailty in survival analysis models (parametric frailty, parametric shared frailty, and frailty in Cox models

Abstract

Frailty models are used to model survival times in the presence of overdispersion or group-specific random effects. The latter are distinguished from the former by the term "shared" frailty models. With the release of Stata 7, estimation of parametric non-shared frailty models is now possible, and the new models appear as extensions to the six parametric survival models previously available. The overdispersion in this case is represented by an unobservable multiplicative effect on the hazard, or frailty. For purposes of estimation this frailty is then assumed to either follow a gamma or inverse-Gaussian distribution. Parametric shared frailty models are the next logical step in the development in this area, and will soon be available as an update to Stata 7. For these models, the random unobservable frailty effects are assumed to follow either a gamma or inverse-Gaussian distribution, but are constrained to be equal over those observations from a given group or panel. Frailty models and shared frailty models for parametric regression with survival data will be discussed, along with avenues for future development at Stata Corp. in this area, in particular, an application of the frailty principle to Cox regression. Series: United Kingdom Stata Users' Group Meeting, 2001