Parametric Frailty and Shared Frailty Survival Models

Abstract

Frailty models are the survival data analog to regression models, which account for heterogeneity and random effects. A frailty is a latent multiplicative effect on the hazard function and is assumed to have unit mean and variance θ, which is estimated along with the other model parameters. A frailty model is an heterogeneity model where the frailties are assumed to be individual- or spell-specific. A shared frailty model is a random effects model where the frailties are common (or shared) among groups of individuals or spells and are randomly distributed across groups. Parametric frailty models were made available in Stata with the release of Stata 7, while parametric shared frailty models were made available in a recent series of updates. This article serves as a primer to those fitting parametric frailty models in Stata via the streg command. Frailty models are compared to shared frailty models, and both are shown to be equivalent in certain situations. The user-specified form of the distribution of the frailties (whether gamma or inverse Gaussian) is shown to subtly affect the interpretation of the results. Methods for obtaining predictions that are either conditional or unconditional on the frailty are discussed. An example that analyzes the time to recurrence of infection after catheter insertion in kidney patients is studied.