A survival model with Birnbaum–Saunders frailty for uncensored and censored cancer data

Jeremias Leão, Víctor Leiva, Helton Saulo, Vera Tomazella

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Survival models with frailty are used when additional data are non-available to explain the occurrence time of an event of interest. This non-availability may be considered as a random effect related to unobserved explanatory variables, or that cannot be measured, often attributed to environmental or genetic factors. We propose a survival model with frailty based on the Birnbaum–Saunders distribution. This distribution has been widely applied to lifetime data. The random effect is the frailty, which is assumed to follow the Birnbaum–Saunders distribution and introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters and evaluate its performance under different censoring proportions by a Monte Carlo simulation study. Two types of residuals are considered to assess the adequacy of the proposed model. Examples with uncensored and censored real-world data sets illustrate the potential applications of the proposed model.

Original languageEnglish
Pages (from-to)707-729
Number of pages23
JournalBrazilian Journal of Probability and Statistics
Issue number4
StatePublished - Nov 2018


  • Birnbaum-Saunders distribution
  • Frailty models
  • Likelihood methods
  • Medical data
  • Monte carlo simulation
  • R software


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