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The log-beta Weibull regression model with application to predict recurrence of prostate cancer

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  • Edwin Ortega
  • Gauss Cordeiro
  • Michael Kattan

Abstract

We study the properties of the called log-beta Weibull distribution defined by the logarithm of the beta Weibull random variable (Famoye et al. in J Stat Theory Appl 4:121–136, 2005 ; Lee et al. in J Mod Appl Stat Methods 6:173–186, 2007 ). An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We obtain formal expressions for the moments, moment generating function, quantile function and mean deviations. We construct a regression model based on the new distribution to predict recurrence of prostate cancer for patients with clinically localized prostate cancer treated by open radical prostatectomy. It can be applied to censored data since it represents a parametric family of models that includes as special sub-models several widely-known regression models. The regression model was fitted to a data set of 1,324 eligible prostate cancer patients. We can predict recurrence free probability after the radical prostatectomy in terms of highly significant clinical and pathological explanatory variables associated with the recurrence of the disease. The predicted probabilities of remaining free of cancer progression are calculated under two nested models. Copyright Springer-Verlag 2013

Suggested Citation

  • Edwin Ortega & Gauss Cordeiro & Michael Kattan, 2013. "The log-beta Weibull regression model with application to predict recurrence of prostate cancer," Statistical Papers, Springer, vol. 54(1), pages 113-132, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:113-132
    DOI: 10.1007/s00362-011-0414-1
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    References listed on IDEAS

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    1. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Cancho, Vicente G. & Cordeiro, Gauss M., 2010. "The log-exponentiated Weibull regression model for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1017-1035, April.
    2. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    3. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
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    Cited by:

    1. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    2. Badmus NI & Amusa SO & Akinsanya T & Okorafor U, 2018. "An Empirical Regression Approach to Estimating Blood Pressure Components," International Journal of Cell Science & Molecular Biology, Juniper Publishers Inc., vol. 4(4), pages 75-80, May.
    3. Indranil Ghosh & Saralees Nadarajah, 2017. "On some further properties and application of Weibull-R family of distributions," Papers 1711.00171, arXiv.org.
    4. Gauss M. Cordeiro & Elisângela C. Biazatti & Luís H. de Santana, 2023. "A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data," Stats, MDPI, vol. 6(2), pages 1-17, May.
    5. Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.
    6. Indranil Ghosh & Saralees Nadarajah, 2018. "On Some Further Properties and Application of Weibull-R Family of Distributions," Annals of Data Science, Springer, vol. 5(3), pages 387-399, September.

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