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Research Article

Defective 3-parameter Gompertz model with frailty term for estimating cure fraction in survival data

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Pages 90-113 | Received 29 Jan 2021, Accepted 29 Apr 2022, Published online: 07 Jun 2022

References

  • Achcar, J. A., E. Z. Martinez, B. C. de Freitas, M. V. D. O. Peres, et al. 2021. Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction. Pakistan Journal of Statistics and Operation Research 467–481. doi:10.18187/pjsor.v17i2.3693.
  • Balka, J., A. F. Desmond, and P. D. McNicholas. 2009. Review and implementation of cure models based on first hitting times for wiener processes. Lifetime Data Analysis 15 (2):147. doi:10.1007/s10985-008-9108-y.
  • Balka, J., A. F. Desmond, and P. D. McNicholas. 2011. Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models. Journal of Applied Statistics 38 (1):127–144. doi:10.1080/02664760903301127.
  • Berkson, J., and R. P. Gage. 1952. Survival curve for cancer patients following treatment. Journal of the American Statistical Association 47 (259):501–515. doi:10.1080/01621459.1952.10501187.
  • Boag, J. W. 1949. Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society Series B 15–53.
  • Bogani, G., V. Di Donato, F. Sopracordevole, A. Ciavattini, A. Ghelardi, S. Lopez, T. Simoncini, F. Plotti, J. Casarin, and M. Serati. 2020. Recurrence rate after loop electrosurgical excision procedure (LEEP) and laser conization: A 5-year follow-up study. Gynecologic Oncology 159 (3):636–641. doi:10.1016/j.ygyno.
  • Borges, P. 2017. EM algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with long-term survivors: An application to uterine cervical cancer data. Journal of Statistical Computation and Simulation 87 (9):1712–1722. doi:10.1080/00949655.2017.1281927.
  • Cantor, A. B., and J. J. Shuster. 1992. Parametric versus non‐parametric methods for estimating cure rates based on censored survival data. Statistics in Medicine 11 (7):931–937. doi:10.1002/sim.4780110710.
  • Dos Santos, M. R., J. A. Achcar, and E. Z. Martinez. 2017. Bayesian and maximum likelihood inference for the defective Gompertz cure rate model with covariates: An application to the cervical carcinoma study. Ciência e Natura 39 (2):244–258. doi:10.5902/2179460X24118.
  • Elbers, C., and G. Ridder. 1982. True and spurious duration dependence: The identifiability of the proportional hazard model. Review of Economic Studies 49 (3):403–409. doi:10.2307/2297364.
  • Farzaneh, F., N. Faghih, M. S. Hosseini, M. Arab, T. Ashrafganjoei, A. Bahman, et al. 2019. Evaluation of neutrophil–lymphocyte ratio as a prognostic factor in cervical intraepithelial neoplasia recurrence. Asian Pacific Journal of Cancer Prevention 20 (8):2365–2372. doi:10.31557/APJCP.2019.20.8.2365.
  • Gieser, P. W., M. N. Chang, P. V. Rao, J. J. Shuster, J. Pullen, et al. 1998. Modelling cure rates using the Gompertz model with covariate information. Statistics in Medicine 17 (8):831–839. doi:10.1002/(SICI)1097-0258(19980430)17:8<831::AID-SIM790>3.0.CO;2-G.
  • Haile, S. R., J. H. Jeong, X. Chen, Y. Cheng, et al. 2016. A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data. Journal of Applied Statistics. 43(12):2239–2253. doi:10.1080/02664763.2015.1134450.
  • Haybittle, J. L. 1959. The estimation of the proportion of patients cured after treatment for cancer of the breast. British Journal of Radiology 32 (383):725–733. doi:10.1259/0007-1285-32-383-725.
  • Hougaard, P. 1995. Frailty models for survival data. Lifetime Data Analysis 1 (3):255–273. doi:10.1007/BF00985760.
  • Ibrahim, J. G., M. H. Chen, and D. Sinha. 2001. Bayesian semiparametric models for survival data with a cure fraction. Biometrics 57 (2):383–388. doi:10.1111/j.0006-341x.2001.00383.x.
  • Lemeshko, B. Y., S. B. Lemeshko, K. A. Akushkina, et al. 2010. Inverse Gaussian model and its applications in reliability and survival analysis. InMathematical and statistical models and methods in reliability. Boston, MA: Birkhäuser. 433–453.
  • Link, P. P. Your best defense vs. another melanoma. American academy of dermatology association. Link:https://www.thetapattison.com/library/9395/Yourbestdefensevs.anothermelanoma.html
  • Martinez, E. Z., and J. A. Achcar. 2017. The defective generalized Gompertz distribution and its use in the analysis of lifetime data in presence of cure fraction, censored data and covariates. Electronic Journal of Applied Statistical Analysis 10:463–484.
  • Martinez, E. Z., and J. A. Achcar. 2018. A new straightforward defective distribution for survival analysis in the presence of a cure fraction. Journal of Statistical Theory and Practice 12 (4):688–703. doi:10.1080/15598608.2018.1460885.
  • Martinez, E. Z., J. A. Achcar, A. A. Jácome, J. S. Santos, et al. 2013. Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data. Computer Methods and Programs in Biomedicine 112 (3):343–355. doi:10.1016/j.cmpb.2013.07.021.
  • Missov, T. I. 2013. Gamma-Gompertz life expectancy at birth. Demographic Research 28:259–270. doi:10.4054/DemRes.2013.28.9.
  • Peng, Y., and J. M. Taylor. 2017. Residual‐based model diagnosis methods for mixture cure models. Biometrics 73 (2):495–505. doi:10.1111/biom.12582.
  • Price, D. L., and A. K. Manatunga. 2001. Modelling survival data with a cured fraction using frailty models. Statistics in Medicine 20 (9–10):1515–1527. doi:10.1002/sim.687.
  • R core team, R: A language and environment for statistical computing, R foundation for statistical computing Vienna, Austria. Available at http://www.R-project.org/,2016.
  • Rocha, R., S. Nadarajah, V. Tomazella, F. Louzada, et al. 2016. Two new defective distributions based on the Marshall–olkin extension. Lifetime Data Analysis 22 (2):216–240. doi:10.1007/s10985-015-9328-x.
  • Rocha, R., S. Nadarajah, V. Tomazella, F. Louzada, et al. 2017a. A new class of defective models based on the Marshall–olkin family of distributions for cure rate modeling. Computational Statistics & Data Analysis 107:48–63. doi:10.1016/j.csda.2016.10.001.
  • Rocha, R., S. Nadarajah, V. Tomazella, F. Louzada, A. Eudes, et al. 2017b. New defective models based on the Kumaraswamy family of distributions with application to cancer data sets. Statistical Methods in Medical Research 26 (4):1737–1755. doi:10.1177/0962280215587976.
  • Scudilio, J., V. F. Calsavara, R. Rocha, F. Louzada, V. Tomazella, A. S. Rodrigues, et al. 2019. Defective models induced by gamma frailty term for survival data with cured fraction. Journal of Applied Statistics 46 (3):484–507. doi:10.1080/02664763.2018.1498464.
  • Sinha, D., and D. K. Dey. 1997. Semiparametric Bayesian analysis of survival data. Journal of the American Statistical Association 92 (439):1195–1212. doi:10.1080/01621459.1997.10474077.
  • Tsodikov, A. D., J. G. Ibrahim, and A. Y. Yakovlev. 2003. Estimating cure rates from survival data: An alternative to two-component mixture models. Journal of the American Statistical Association 98 (464):1063–1078. doi:10.1198/01622145030000001007.
  • 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):439–454. doi:10.2307/2061224.
  • Whttmore, G. A. 1979. An inverse Gaussian model for labour turnover. Journal of the Royal Statistical Society. Series A 142 (4):468–478. doi:10.2307/2982553.
  • Wienke, A. 2014. Frailty models. Wiley StatsRef: Statistics Reference Online.

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