Frailty-Based Competing Risks Model for Multivariate Survival Data

Malka Gorfine, Li Hsu

Research output: Contribution to journalArticlepeer-review


In this work, we provide a new class of frailty-based competing risks models for clustered failure times data. This class is based on expanding the competing risks model of Prentice et al. (1978,Biometrics34, 541-554) to incorporate frailty variates, with the use of cause-specific proportional hazards frailty models for all the causes. Parametric and nonparametric maximum likelihood estimators are proposed. The main advantages of the proposed class of models, in contrast to the existing models, are: (1) the inclusion of covariates; (2) the flexible structure of the dependency among the various types of failure times within a cluster; and (3) the unspecified within-subject dependency structure. The proposed estimation procedures produce the most efficient parametric and semiparametric estimators and are easy to implement. Simulation studies show that the proposed methods perform very well in practical situations.

Original languageEnglish
Pages (from-to)415-426
Number of pages12
Issue number2
StatePublished - Jun 2011
Externally publishedYes


  • Competing risks
  • Frailty model
  • Multivariate survival analysis
  • Nonparametric maximum likelihood estimator


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