Study of the bivariate survival data using frailty models based on Lévy processes

Alexander Begun, Anatoli Yashin

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Frailty models allow us to take into account the non-observable inhomogeneity of individual hazard functions. Although models with time-independent frailty have been intensively studied over the last decades and a wide range of applications in survival analysis have been found, the studies based on the models with time-dependent frailty are relatively rare. In this paper, we formulate and prove two propositions related to the identifiability of the bivariate survival models with frailty given by a nonnegative bivariate Lévy process. We discuss parametric and semiparametric procedures for estimating unknown parameters and baseline hazard functions. Numerical experiments with simulated and real data illustrate these procedures. The statements of the propositions can be easily extended to the multivariate case.
Original languageEnglish
Pages (from-to)37–67
Number of pages31
JournalAStA Advances in Statistical Analysis
Issue number1
Early online date28 Feb 2018
Publication statusPublished - Mar 2019


  • Frailty
  • Lévy process
  • Bivariate survival function
  • Identifiability

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