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Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models

Author

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  • Jeremy Balka
  • Anthony Desmond
  • Paul McNicholas

Abstract

Failure time models are considered when there is a subpopulation of individuals that is immune, or not susceptible, to an event of interest. Such models are of considerable interest in biostatistics. The most common approach is to postulate a proportion p of immunes or long-term survivors and to use a mixture model [5]. This paper introduces the defective inverse Gaussian model as a cure model and examines the use of the Gibbs sampler together with a data augmentation algorithm to study Bayesian inferences both for the cured fraction and the regression parameters. The results of the Bayesian and likelihood approaches are illustrated on two real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:1:p:127-144
    DOI: 10.1080/02664760903301127
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    Citations

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    Cited by:

    1. 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.
    2. Ricardo Rocha & Saralees Nadarajah & Vera Tomazella & Francisco Louzada, 2016. "Two new defective distributions based on the Marshall–Olkin extension," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 216-240, April.
    3. Rocha, Ricardo & Nadarajah, Saralees & Tomazella, Vera & Louzada, Francisco, 2017. "A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 48-63.
    4. Xu Ruimin & McNicholas Paul D & Desmond Anthony F & Darlington Gerarda A, 2011. "A First Passage Time Model for Long-Term Survivors with Competing Risks," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-15, May.

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