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Weighted Lindley frailty model: estimation and application to lung cancer data

Author

Listed:
  • Alex Mota

    (University of São Paulo
    Federal University of São Carlos
    Federal University of Goiás)

  • Eder A. Milani

    (Federal University of Goiás)

  • Vinicius F. Calsavara

    (A.C.Camargo Cancer Center
    Cedars-Sinai Medical Center)

  • Vera L. D. Tomazella

    (Federal University of São Carlos)

  • Jeremias Leão

    (Federal University of Amazonas)

  • Pedro L. Ramos

    (Pontificia Universidad Católica de Chile)

  • Paulo H. Ferreira

    (Federal University of Bahia)

  • Francisco Louzada

    (University of São Paulo)

Abstract

In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.

Suggested Citation

  • Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:4:d:10.1007_s10985-021-09529-1
    DOI: 10.1007/s10985-021-09529-1
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    References listed on IDEAS

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    1. Almeida, Marco Pollo & Paixão, Rafael S. & Ramos, Pedro L. & Tomazella, Vera & Louzada, Francisco & Ehlers, Ricardo S., 2020. "Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
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    5. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
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