Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

Jeremias Leão, Víctor Leiva, Helton Saulo, Vera Tomazella

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

Original languageEnglish
Pages (from-to)291-314
Number of pages24
JournalBiometrical Journal
Issue number2
StatePublished - 1 Mar 2017


  • Birnbaum–Saunders distribution
  • Censored data
  • Global and local influence
  • Maximum-likelihood method
  • Residual analysis


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