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A model with long-term survivors: negative binomial Birnbaum-Saunders

Author

Listed:
  • Gauss M. Cordeiro
  • Vicente G. Cancho
  • Edwin M. M. Ortega
  • Gladys D. C. Barriga

Abstract

We propose a 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 the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.

Suggested Citation

  • Gauss M. Cordeiro & Vicente G. Cancho & Edwin M. M. Ortega & Gladys D. C. Barriga, 2016. "A model with long-term survivors: negative binomial Birnbaum-Saunders," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1370-1387, March.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:5:p:1370-1387
    DOI: 10.1080/03610926.2013.863929
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    Citations

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    Cited by:

    1. Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.
    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. 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.
    4. 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.

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