IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v43y2016i6p1027-1060.html
   My bibliography  Save this article

Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

Author

Listed:
  • Bao Yiqi
  • Cibele Maria Russo
  • Vicente G. Cancho
  • Francisco Louzada

Abstract

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Negative Binomial distribution and the time to event follows a Weibull distribution. Indeed, we introduce the Weibull-Negative-Binomial (WNB) distribution, which can be used in order to model survival data when the hazard rate function is increasing, decreasing and some non-monotonous shaped. Another advantage of the proposed model is that it has some distributions commonly used in lifetime analysis as particular cases. Moreover, the proposed model includes as special cases some of the well-know cure rate models discussed in the literature. We consider a frequentist analysis for parameter estimation of a WNB model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, the methodology is illustrated on a medical data.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:6:p:1027-1060
    DOI: 10.1080/02664763.2015.1089221
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1089221
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1089221?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. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    2. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    3. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    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. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    6. Hongtu Zhu, 2004. "A diagnostic procedure based on local influence," Biometrika, Biometrika Trust, vol. 91(3), pages 579-589, September.
    7. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    8. 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.
    9. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
    10. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
    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. Yolanda M. Gómez & John L. Santibañez & Vinicius F. Calsavara & Héctor W. Gómez & Diego I. Gallardo, 2024. "A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    2. Alex Mota & Eder A. Milani & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Oilson G. Junior & Vera L. D. Tomazella & Francisco Louzada, 2023. "A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 883-909, September.
    3. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, 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. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    2. 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.
    3. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    4. Mahmoudi, Eisa & Sepahdar, Afsaneh, 2013. "Exponentiated Weibull–Poisson distribution: Model, properties and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 76-97.
    5. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    6. Vicente G. Cancho & Márcia A. C. Macera & Adriano K. Suzuki & Francisco Louzada & Katherine E. C. Zavaleta, 2020. "A new long-term survival model with dispersion induced by discrete frailty," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 221-244, April.
    7. V�ctor Leiva & Emilia Athayde & Cecilia Azevedo & Carolina Marchant, 2011. "Modeling wind energy flux by a Birnbaum--Saunders distribution with an unknown shift parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2819-2838, February.
    8. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    9. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    10. Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    11. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.
    12. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    13. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    14. Beatriz R. Lanjoni & Edwin M. M. Ortega & Gauss M. Cordeiro, 2016. "Extended Burr XII Regression Models: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 203-224, March.
    15. Bobotas, Panayiotis & Koutras, Markos V., 2019. "Distributions of the minimum and the maximum of a random number of random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 57-64.
    16. Mojtaba Alizadeh & Seyyed Fazel Bagheri & Mohammad Alizadeh & Saralees Nadarajah, 2017. "A new four-parameter lifetime distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 767-797, April.
    17. Giovani Carrara Rodrigues & Francisco Louzada & Pedro Luiz Ramos, 2018. "Poisson–exponential distribution: different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 128-144, January.
    18. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    19. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    20. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.

    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:43:y:2016:i:6:p:1027-1060. 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.