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A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data

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  • S. R. Haile
  • J.-H. Jeong
  • X. Chen
  • Y. Cheng

Abstract

The cumulative incidence function is of great importance in the analysis of survival data when competing risks are present. Parametric modeling of such functions, which are by nature improper, suggests the use of improper distributions. One frequently used improper distribution is that of Gompertz, which captures only monotone hazard shapes. In some applications, however, subdistribution hazard estimates have been observed with unimodal shapes. An extension to the Gompertz distribution is presented which can capture unimodal as well as monotone hazard shapes. Important properties of the proposed distribution are discussed, and the proposed distribution is used to analyze survival data from a breast cancer clinical trial.

Suggested Citation

  • S. R. Haile & J.-H. Jeong & X. Chen & Y. Cheng, 2016. "A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2239-2253, September.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:12:p:2239-2253
    DOI: 10.1080/02664763.2015.1134450
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    References listed on IDEAS

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    1. Cheng Yu, 2009. "Modeling Cumulative Incidences of Dementia and Dementia-Free Death Using a Novel Three-Parameter Logistic Function," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-19, November.
    2. Jong‐Hyeon Jeong & Jason Fine, 2006. "Direct parametric inference for the cumulative incidence function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 187-200, April.
    3. Jan Beyersmann & Martin Schumacher, 2008. "A note on nonparametric quantile inference for competing risks and more complex multistate models," Biometrika, Biometrika Trust, vol. 95(4), pages 1006-1008.
    4. L. Peng & J. P. Fine, 2007. "Nonparametric quantile inference with competing–risks data," Biometrika, Biometrika Trust, vol. 94(3), pages 735-744.
    5. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
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    Cited by:

    1. Shama, M.S. & Dey, Sanku & Altun, Emrah & Afify, Ahmed Z., 2022. "The Gamma–Gompertz distribution: Theory and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 689-712.

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