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Bayesian survival model induced by frailty for lifetime with long‐term survivors

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  • Vicente G. Cancho
  • Gladys D. C. Barriga
  • Gauss M. Cordeiro
  • Edwin M. M. Ortega
  • Adriano K. Suzuki

Abstract

It is introduced the proportional hazards frailty model to allow a discrete distribution for the frailty variable. Frailty zero can be interpreted as being immune or cured. It is defined a class of survival models induced by a discrete frailty having a mixed Poisson distribution, which can account for unobserved dispersion. Further, a new regression to evaluate the effects of covariates in the cure fraction is constructed. Several former cure survival models are special cases of the proposed modeling framework. The inferential approach is based on Bayesian methods. Some simulation results are provided to assess the performance of the new regression. Its importance is illustrated by means of an application to colorectal cancer data.

Suggested Citation

  • Vicente G. Cancho & Gladys D. C. Barriga & Gauss M. Cordeiro & Edwin M. M. Ortega & Adriano K. Suzuki, 2021. "Bayesian survival model induced by frailty for lifetime with long‐term survivors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 299-323, August.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:3:p:299-323
    DOI: 10.1111/stan.12236
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    References listed on IDEAS

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    1. Vicente Cancho & Josemar Rodrigues & Mario de Castro, 2011. "A flexible model for survival data with a cure rate: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 57-70.
    2. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2002. "Bayesian Inference for Multivariate Survival Data with a Cure Fraction," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 101-126, January.
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    4. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    5. Cancho, Vicente G. & Dey, Dipak K. & Lachos, Victor H. & Andrade, Marinho G., 2011. "Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 588-602, January.
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    Cited by:

    1. Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.

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