A bivariate survival model with compound Poisson frailty

Stat Med. 2010 Jan 30;29(2):275-83. doi: 10.1002/sim.3749.


A correlated frailty model is suggested for analysis of bivariate time-to-event data. The model is an extension of the correlated power variance function (PVF) frailty model (correlated three-parameter frailty model) (J. Epidemiol. Biostat. 1999; 4:53-60). It is based on a bivariate extension of the compound Poisson frailty model in univariate survival analysis (Ann. Appl. Probab. 1992; 4:951-972). It allows for a non-susceptible fraction (of zero frailty) in the population, overcoming the common assumption in survival analysis that all individuals are susceptible to the event under study. The model contains the correlated gamma frailty model and the correlated inverse Gaussian frailty model as special cases. A maximum likelihood estimation procedure for the parameters is presented and its properties are studied in a small simulation study. This model is applied to breast cancer incidence data of Swedish twins. The proportion of women susceptible to breast cancer is estimated to be 15 per cent.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Age of Onset
  • Aged
  • Aged, 80 and over
  • Algorithms
  • Breast Neoplasms / epidemiology
  • Computer Simulation
  • Epidemiologic Research Design
  • Female
  • Humans
  • Likelihood Functions
  • Middle Aged
  • Models, Statistical*
  • Poisson Distribution
  • Proportional Hazards Models
  • Survival Analysis*
  • Sweden / epidemiology
  • Twin Studies as Topic