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The Poisson–Inverse-Gaussian regression model with cure rate: a Bayesian approach and its case influence diagnostics

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  • Adriano Suzuki
  • Vicente Cancho
  • Francisco Louzada

Abstract

This paper proposes a new survival model, called Poisson Inverse-Gaussian regression cure rate model (PIGcr), which enables different underlying activation mechanisms that lead to the event of interest. The number of competing causes of the event of interest follows a Poisson distribution and the time for the event follows an Inverse-Gaussian distribution. The model takes into account the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo was considered. Discussions on the model selection criteria, as well as a case deletion influence diagnostics are addressed for a joint posterior distribution based on the $$\psi $$ ψ -divergence, which has several divergence measures as particular cases, such as Kullback–Leibler (K–L), $$J$$ J -distance, $$L_1$$ L 1 norm and $$\chi ^2$$ χ 2 -square divergence measures. The procedures are illustrated in artificial and real data. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Adriano Suzuki & Vicente Cancho & Francisco Louzada, 2016. "The Poisson–Inverse-Gaussian regression model with cure rate: a Bayesian approach and its case influence diagnostics," Statistical Papers, Springer, vol. 57(1), pages 133-159, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:133-159
    DOI: 10.1007/s00362-014-0649-8
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    References listed on IDEAS

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    7. 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.
    8. Samuel Kotz & Víctor Leiva & Antonio Sanhueza, 2010. "Two New Mixture Models Related to the Inverse Gaussian Distribution," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 199-212, March.
    9. Jeremy Balka & Anthony Desmond & Paul McNicholas, 2011. "Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 127-144.
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    11. Cynthia Tojeiro & Francisco Louzada, 2012. "A general threshold stress hybrid hazard model for lifetime data," Statistical Papers, Springer, vol. 53(4), pages 833-848, November.
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