The Identifiability of Dependent Competing Risks Models Induced by Bivariate Frailty Models

Antai Wang, Krishnendu Chandra, Ruihua Xu, Junfeng Sun

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we propose to use a special class of bivariate frailty models to study dependent censored data. The proposed models are closely linked to Archimedean copula models. We give sufficient conditions for the identifiability of this type of competing risks models. The proposed conditions are derived based on a property shared by Archimedean copula models and satisfied by several well-known bivariate frailty models. Compared with the models studied by Heckman and Honoré and Abbring and van den Berg, our models are more restrictive but can be identified with a discrete (even finite) covariate. Under our identifiability conditions, expectation-maximization (EM) algorithm provides us with consistent estimates of the unknown parameters. Simulation studies have shown that our estimation procedure works quite well. We fit a dependent censored leukaemia data set using the Clayton copula model and end our paper with some discussions.

Original languageEnglish (US)
Pages (from-to)427-437
Number of pages11
JournalScandinavian Journal of Statistics
Issue number2
StatePublished - Jun 1 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Archimedean copula models
  • Bivariate frailty models
  • Competing risks models
  • Discrete covariates
  • Identifiability


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