IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v39y2012i6p1191-1210.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2011.644525
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2011.644525?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    2. Bao Yiqi & Cibele Maria Russo & Vicente G. Cancho & Francisco Louzada, 2016. "Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(6), pages 1027-1060, May.
    3. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. Suvra Pal & N. Balakrishnan, 2017. "Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data," Computational Statistics, Springer, vol. 32(2), pages 429-449, June.
    5. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    6. Hattori, Satoshi & Kato, Mai, 2009. "Approximate subject-deletion influence diagnostics for Inverse Probability of Censoring Weighted (IPCW) method," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1833-1838, September.
    7. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    8. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    9. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    10. Sileshi, Gudeta & Hailu, Girma & Nyadzi, Gerson I., 2009. "Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data," Ecological Modelling, Elsevier, vol. 220(15), pages 1764-1775.
    11. Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 270-284.
    12. Hassan M. Okasha & Abdulkareem M. Basheer & A. H. El-Baz, 2021. "Marshall–Olkin Extended Inverse Weibull Distribution: Different Methods of Estimations," Annals of Data Science, Springer, vol. 8(4), pages 769-784, December.
    13. Ilhan Usta, 2013. "Different estimation methods for the parameters of the extended Burr XII distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 397-414, February.
    14. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    15. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    16. 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.
    17. Hassan S. Bakouch & Abdus Saboor & Muhammad Nauman Khan, 2021. "Modified Beta Linear Exponential Distribution with Hydrologic Applications," Annals of Data Science, Springer, vol. 8(1), pages 131-157, March.
    18. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    19. Krishna K. Saha & Roger Bilisoly & Darius M. Dziuda, 2014. "Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 439-453, February.
    20. Seoyun Choe & Hee-Sung Kim & Sunmi Lee, 2020. "Exploration of Superspreading Events in 2015 MERS-CoV Outbreak in Korea by Branching Process Models," IJERPH, MDPI, vol. 17(17), pages 1-14, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:39:y:2012:i:6:p:1191-1210. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.