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A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling

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  • Rocha, Ricardo
  • Nadarajah, Saralees
  • Tomazella, Vera
  • Louzada, Francisco

Abstract

Defective distributions model cure rates by changing the usual domain of its parameters in a way that their survival functions converge to a value p∈(0,1). A new way to generate defective distributions to model cure fractions is proposed. The new way relies on a property derived from the Marshall–Olkin family of distributions. To exemplify this new result we use the extended Weibull distribution and introduce ten new defective distributions. A regression approach for these models is also proposed. Estimation by maximum likelihood is discussed and their asymptotes verified through simulations. Practical use is illustrated by applications to four real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:107:y:2017:i:c:p:48-63
    DOI: 10.1016/j.csda.2016.10.001
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    References listed on IDEAS

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    1. N. Balakrishnan & Suvra Pal, 2015. "An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods," Computational Statistics, Springer, vol. 30(1), pages 151-189, March.
    2. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    3. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    4. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    5. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    6. 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.
    7. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
    8. Joseph G. Ibrahim & Ming-Hui Chen & Debajyoti Sinha, 2001. "Bayesian Semiparametric Models for Survival Data with a Cure Fraction," Biometrics, The International Biometric Society, vol. 57(2), pages 383-388, June.
    9. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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    Cited by:

    1. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.

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