Cure rate and statistical inference for the Marshall-Olkin generalized defective Gompertz distribution under censored survival data
*Tasnime HamdeniCorresponding authorhamdeni.tasnime@gmail.comDepartment of Applied Mathematics Higher Engineering Schools of Tunis University of Tunis El-Manar Laboratoire Signal Image et Maitrise de l’Energie (LR13ES03)Tunis, TunisiaView full profile → , Soufiane Gasmisoufiane.kasmi3@gmail.comDepartment of Mathematics Higher National Engineering School of Tunis University of Tunis Laboratoire Modélisation Mathématique analyse Harmonique et théorie de potentiel (LR18ES09)Tunis, TunisiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 Dec 2021
- Accepted:
- 07 Jun 2022
- Published Online:
- 01 Mar 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JSMS-978
- Pages:
- 257–266
Abstract
Keywords
Subject Classifications
References
[1] J. W. Boag, “Maximum likelihood estimates of the proportion of patients cured by cancer therapy,” J. Roy. Stat. Soc. Ser. B (Methodol.), vol. 11, no. 1, pp. 15–53 (1949).
[2] P. Borges, “EM algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with longterm survivors: an application to uterine cervical cancer data,” J. Stat. Comput. Simul., vol. 87, no. 9, pp. 1712–1722 (2017).
[3] A. B. Cantor and J. J. Shuster, “Parametric versus non-parametric methods for estimating cure rates based on censored survival data,” Stat. Med., vol. 11, no. 7, pp. 931–937 (1992).
[4] S. Dey, F. A. Moala, and D. Kumar, “Statistical properties and different methods of estimation of Gompertz distribution with application,” J. Stat. Manag. Syst., vol. 21, no. 5, pp. 839–876 (2018).
[5] M. Dhar and P. Bhattacharya, “Comparison of the logistic and the Gompertz curve under different constraints,” J. Stat. Manag. Syst., vol. 21, no. 7, pp. 1189–1210 (2018).
[6] A. El-Gohary, A. Alshamrani, and A. N. Al-Otaibi, “The generalized Gompertz distribution,” Appl. Math. Model., vol. 37, no. 1-2, pp. 13–24 (2013).
[7] B. Gompertz, “XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, in a letter to Francis Baily, Esq. FRS &c.,” Philos. Trans. Royal Soc. London, vol. 115, pp. 513–583 (1825).
[8] T. Hamdeni and S. Gasmi, “The Marshall–Olkin generalized defective Gompertz distribution for surviving fraction modeling,” Commun. Stat. Simul. Comput., pp. 1–14 (2020a).
[9] T. Hamdeni and S. Gasmi, “A proportional-hazards model for survival analysis and long-term survivors modeling: Application to amyotrophic lateral sclerosis data,” J. Appl. Stat., vol. 47, no. 16, pp. 2904–2921 (2020b), doi: 10.1080/02664763.2020.1830954.
[10] P. C. Lambert, P. W. Dickman, C. L. Weston, and J. R. Thompson, “Estimating the cure fraction in population-based cancer studies by using finite mixture models,” J. Royal Stat. Soc. Ser. C (Appl. Stat.), vol. 59, no. 1, pp. 35–55 (2010).
[11] A. W. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families,” Biometrika, vol. 84, no. 3, pp. 641–652 (1997).
[12] E. Z. Martinez and J. A. Achcar, “The defective generalized Gompertz distribution and its use in the analysis of lifetime data in presence of cure fraction, censored data, and covariates,” Electron. J. Appl. Stat. Anal., vol. 10, no. 2, pp. 463–484 (2017).
[13] W. Nissas and S. Gasmi, “A hybrid decision dependent maintenance model of failure rate and virtual age classes using modified Weibull intensity,” Communications in Statistics-Simulation and Computation, pp. 1–15 (2019).
[14] R. Rocha, S. Nadarajah, V. Tomazella, and F. Louzada, “A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling,” Computational Statistics & Data Analysis, vol. 107, pp. 48–63 (2017).



