Frailty models for survival data
 Philip Hougaard
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A frailty model is a random effects model for time variables, where the random effect (the frailty) has a multiplicative effect on the hazard. It can be used for univariate (independent) failure times, i.e. to describe the influence of unobserved covariates in a proportional hazards model. More interesting, however, is to consider multivariate (dependent) failure times generated as conditionally independent times given the frailty. This approach can be used both for survival times for individuals, like twins or family members, and for repeated events for the same individual. The standard assumption is to use a gamma distribution for the frailty, but this is a restriction that implies that the dependence is most important for late events. More generally, the distribution can be stable, inverse Gaussian, or follow a power variance function exponential family. Theoretically, large differences are seen between the choices. In practice, using the largest model makes it possible to allow for more general dependence structures, without making the formulas too complicated.
 Title
 Frailty models for survival data
 Journal

Lifetime Data Analysis
Volume 1, Issue 3 , pp 255273
 Cover Date
 199509
 DOI
 10.1007/BF00985760
 Print ISSN
 13807870
 Online ISSN
 15729249
 Publisher
 Kluwer Academic Publishers
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 Authors

 Philip Hougaard ^{(1)}
 Author Affiliations

 1. Novo Nordisk, Novo Alle, DK2880, Bagsvaerd, Denmark