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Article

Generalized Birnbaum–Saunders mixture cure frailty model: inferential method and an application to bone marrow transplant data

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Pages 5655-5679 | Received 11 Jun 2021, Accepted 14 Oct 2021, Published online: 02 Nov 2021

References

  • Aalen, O. O. 1988. Heterogeneity in survival analysis. Statistics in Medicine 7 (11):1121–37. doi:10.1002/sim.4780071105.
  • Aalen, O. O. 1992. Modelling heterogeneity in survival analysis by the compound Poisson distribution. Annals of Applied Probability 2 (4):951–72.
  • Balakrishnan, N., and D. Kundu. 2019. Birnbaum-Saunders distribution: A review of models, analysis, and applications. Applied Stochastic Models in Business and Industry 35 (1):4–132. (with discussion). doi:10.1002/asmb.2348.
  • Balakrishnan, N., and K. Liu. 2018. Semi-parametric likelihood inference for Birnbaum-Saunders frailty model. Revstat – Statistical Journal 16 (2):231–55.
  • Balakrishnan, N., and Y. Peng. 2006. Generalized gamma frailty model. Statistics in Medicine 25 (16):2797–816. doi:10.1002/sim.2375.
  • Berkson, J., and R. P. Gage. 1952. Survival curve for cancer patients following treatment. Journal of the American Statistical Association 47 (259):501–15. doi:10.1080/01621459.1952.10501187.
  • Díaz-García, J. A., and V. Leiva. 2007. A new family of life distributions based on the elliptically contoured distributions. Journal of Statistical Planning and Inference 137 (4):1512–3. doi:10.1016/j.jspi.2006.06.040.
  • Hougaard, P. 1984. Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika 71 (1):75–83. doi:10.1093/biomet/71.1.75.
  • Hougaard, P. 1986a. A class of multivanate failure time distributions. Biometrika 73 (3):671–8. doi:10.1093/biomet/73.3.671.
  • Hougaard, P. 1986b. Survival models for heterogeneous populations derived from stable distributions. Biometrika 73 (2):387–96. doi:10.1093/biomet/73.2.387.
  • Kersey, J. H., D. Weisdorf, M. E. Nesbit, T. W. LeBien, W. G. Woods, P. B. McGlave, T. Kim, D. A. Vallera, A. I. Goldman, and B. Bostrom. 1987. Comparison of autologous and allogeneic bone marrow transplantation for treatment of high-risk refractory acute lymphoblastic leukemia. The New England Journal of Medicine 317 (8):461–7. doi:10.1056/NEJM198708203170801.
  • Kheiri, S., A. Kimber, and M. R. Meshkani. 2007. Bayesian analysis of an inverse Gaussian correlated frailty model. Computational Statistics & Data Analysis 51 (11):5317–26. doi:10.1016/j.csda.2006.09.026.
  • Kim, Y. J. 2020. Joint model for recurrent event data with a cured fraction and a terminal event. Biometrical Journal. Biometrische Zeitschrift 62 (1):24–33. doi:10.1002/bimj.201800321.
  • Klein, J. P. 1992. Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 48 (3):795–806. doi:10.2307/2532345.
  • Leão, J., V. Leiva, H. Saulo, and V. Tomazella. 2017. Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data. Biometrical Journal. Biometrische Zeitschrift 59 (2):291–314. doi:10.1002/bimj.201600008.
  • Leão, J., V. Leiva, H. Saulo, and V. Tomazella. 2018a. A survival model with Birnbaum-Saunders frailty for uncensored and censored cancer data. Brazilian Journal of Probability and Statistics 32 (4):707–29. doi:10.1214/17-BJPS360.
  • Leão, J., V. Leiva, H. Saulo, and V. Tomazella. 2018b. Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data. Statistics in Medicine 37 (29):4421–40. doi:10.1002/sim.7929.
  • Leiva, V., M. Barros, G. A. Paula, and A. Sanhueza. 2008a. Generalized Birnbaum-Saunders distributions applied to air pollutant concentration. Environmetrics 19 (3):235–49. doi:10.1002/env.861.
  • Leiva, V., M. Riquelme, N. Balakrishnan, and A. Sanhueza. 2008b. Lifetime analysis based on the generalized Birnbaum–Saunders distribution. Computational Statistics & Data Analysis 52 (4):2079–97. doi:10.1016/j.csda.2007.07.003.
  • Maller, R. A., and S. Zhou. 1995. Testing for the presence of immune or cured individuals in censored survival data. Biometrics 51 (4):1197–205. doi:10.2307/2533253.
  • McGilchrist, C., and C. Aisbett. 1991. Regression with frailty in survival analysis. Biometrics 47 (2):461–6. doi:10.2307/2532138.
  • Meshkat, M.,. A. R. Baghestani, F. Zayeri, M. Khayamzadeh, and M. E. Akbari. 2018. Survival probability and prognostic factors of Iranian breast cancer patients using cure rate model. The Breast Journal 24 (6):1015–8. doi:10.1111/tbj.13120.
  • Pal, S., and N. Balakrishnan. 2018. Expectation maximization algorithm for Box-Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes. IEEE Journal of Biomedical and Health Informatics 22 (3):926–34. doi:10.1109/JBHI.2017.2704920.
  • Peng, Y., K. B. Dear, and K. Carriere. 2001. Testing for the presence of cured patients: A simulation study. Statistics in Medicine 20 (12):1783–96. doi:10.1002/sim.781.
  • Peng, Y., and J. Zhang. 2008. Estimation method of the semiparametric mixture cure gamma frailty model. Statistics in Medicine 27 (25):5177–94. doi:10.1002/sim.3358.
  • Price, D. L., and A. K. Manatunga. 2001. Modelling survival data with a cured fraction using frailty models. Statistics in Medicine 20 (9-10):1515–27. doi:10.1002/sim.687.
  • Rondeau, V., E. Schaffner, F. Corbière, J. R. Gonzalez, and S. Mathoulin-Pélissier. 2013. Cure frailty models for survival data: Application to recurrences for breast cancer and to hospital readmissions for colorectal cancer. Statistical Methods in Medical Research 22 (3):243–60. doi:10.1177/0962280210395521.
  • Sanhueza, A., V. Leiva, and N. Balakrishnan. 2008. The generalized Birnbaum–Saunders distribution and its theory, methodology, and application. Communications in Statistics – Theory and Methods 37 (5):645–70. doi:10.1080/03610920701541174.
  • Schneider, S., F. N. Demarqui, E. A. Colosimo, and V. D. Mayrink. 2020. An approach to model clustered survival data with dependent censoring. Biometrical Journal. Biometrische Zeitschrift 62 (1):157–74. doi:10.1002/bimj.201800391.
  • Vaupel, J. W., K. G. Manton, and E. Stallard. 1979. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16 (3):439–54.
  • Zhang, J., and Y. Peng. 2007. A new estimation method for the semiparametric accelerated failure time mixture cure model. Statistics in Medicine 26 (16):3157–71. doi:10.1002/sim.2748.

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