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The negative binomial--beta Weibull regression model to predict the cure of prostate cancer

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  • Edwin M.M. Ortega
  • Gauss M. Cordeiro
  • Michael W. Kattan

Abstract

In this article, for the first time, we propose the negative binomial--beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

Suggested Citation

  • Edwin M.M. Ortega & Gauss M. Cordeiro & Michael W. Kattan, 2012. "The negative binomial--beta Weibull regression model to predict the cure of prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1191-1210, November.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:6:p:1191-1210
    DOI: 10.1080/02664763.2011.644525
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    1. 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.
    2. Hongtu Zhu, 2004. "A diagnostic procedure based on local influence," Biometrika, Biometrika Trust, vol. 91(3), pages 579-589, September.
    3. 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.
    4. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
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    1. Morad Alizadeh & S. M. T. K. MirMostafee & Edwin M. M. Ortega & Thiago G. Ramires & Gauss M. Cordeiro, 2017. "The odd log-logistic logarithmic generated family of distributions with applications in different areas," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.

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