Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Bayesian cure rate model with dispersion induced by discrete frailty

  • Cancho, Vicente G. (Department of Applied Mathematics and Statistics, University of Sao Paulo) ;
  • Zavaleta, Katherine E.C. (Department of Statistics, Federal University of Sao Carlos) ;
  • Macera, Marcia A.C. (Department of Applied Mathematics and Statistics, University of Sao Paulo) ;
  • Suzuki, Adriano K. (Department of Applied Mathematics and Statistics, University of Sao Paulo) ;
  • Louzada, Francisco (Department of Applied Mathematics and Statistics, University of Sao Paulo)
  • Received : 2018.02.20
  • Accepted : 2018.08.21
  • Published : 2018.09.30
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Abstract

In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ${\psi}-divergence$ measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.

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References

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