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

References

• Boag JW. Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc B. 1949;11:15–53.
   Google Scholar
• Berkson J, Gage RP. Survival curve for cancer patients following treatment. J Amer Statist Assoc. 1952;42:501–515. doi: 10.1080/01621459.1952.10501187
   Google Scholar
• Maller R, Zhou X. Testing for the presence of immune or cured individuals in censored survival data. Biometrics. 1995;51:1197–1205. doi: 10.2307/2533253
   PubMed Web of Science ®Google Scholar
• Balka J, Desmond AF, McNicholas PD. Review and implementation of cure models based on first hitting times for wiener processes. Lifetime Data Anal. 2009;15:147–176. doi: 10.1007/s10985-008-9108-y
   PubMed Web of Science ®Google Scholar
• Balka J, Desmond AF, McNicholas PD. Bayesian and likelihood inference for cure rates based on defective inverse gaussian regression models. J Appl Stat. 2011;38:127–144. doi: 10.1080/02664760903301127
   Web of Science ®Google Scholar
• Rocha R, Nadarajah S, Tomazella V, et al. New defective models based on the Kumaraswamy family of distributions with application to cancer data sets. Stat Methods Med Res. 2015. doi:doi: 10.1177/0962280215587976
   Google Scholar
• Cordeiro GM, Castro M. A new family of generalized distributions. J Stat Comput Simul. 2011;81:883–898. doi: 10.1080/00949650903530745
   Web of Science ®Google Scholar
• Gompertz B. On the nature of the function expressive of the law of human mortality and on the new mode of determining the value of life contingencies. Philos Trans R Soc A. 1825;115:513–580. doi: 10.1098/rstl.1825.0026
   Google Scholar
• Read CB. Gompertz distribution. Encyclopedia of statistical sciences. New York: Wiley; 1983.
   Google Scholar
• Makany R. A theoretical basis of Gompertz's curve. Biom J. 1991;33:121–128. doi: 10.1002/bimj.4710330115
   Web of Science ®Google Scholar
• Franses PH. Fitting a Gompertz curve. J Oper Res Soc. 1994;45:109–113. doi: 10.1057/jors.1994.11
   Web of Science ®Google Scholar
• Chen Z. Parameter estimation of the Gompertz population. Biom J. 1997;39:117–124. doi: 10.1002/bimj.4710390111
   Web of Science ®Google Scholar
• Gieser PW, Chang MN, Rao PV, et al. Modelling cure rates using the Gompertz model with covariate information. Stat Med. 1998;17:831–839. doi: 10.1002/(SICI)1097-0258(19980430)17:8<831::AID-SIM790>3.0.CO;2-G
   PubMed Web of Science ®Google Scholar
• Wu JW, Hung WL, Tsai CH. Estimation of parameters of the Gompertz distribution using the least squares method. Appl Math Comput. 2004;158:133–147.
   Web of Science ®Google Scholar
• El-Gohary A, Alshamrani A, Al-Otaibi AN. The generalized Gompertz distribution. Appl Math Model. 2013;37:13–24. doi: 10.1016/j.apm.2011.05.017
   Web of Science ®Google Scholar
• Ahmed EA. Estimation of some lifetime parameters of generalized Gompertz distribution under progressively type-II censored data. Appl Math Model. 2015;39:5567–5578. doi: 10.1016/j.apm.2015.01.023
   Web of Science ®Google Scholar
• Gupta RD, Kundu D. Generalized exponential distribution. Aust N Z J Stat. 1999;41:173–188. doi: 10.1111/1467-842X.00072
   Web of Science ®Google Scholar
• Cox DR. Regression models and life-tables (with discussion). J R Stat Soc Ser B. 1972;34:187–220.
   Web of Science ®Google Scholar
• McLachlan G, Krishnan T. The EM algorithm and extensions. 2nd ed. New York: John Wiley & Sons; 2008.
   Google Scholar
• Lange K. A gradient algorithm locally equivalent to the EM algorithm. J R Stat Soc Ser B. 1995;57:425–437.
   Google Scholar
• Dempster A, Laird N, Rubim D. Maximum likelihood from incomplete data via the EM algorithm (with discussion). J R Stat Soc Ser B. 1977;39:1–38.
   Google Scholar
• Balakrishnan N, Mitra D. Left truncated and right censored Weibull data and likelihood inference with an illustration. Comput Statist Data Anal. 2012;56:4011–4025. doi: 10.1016/j.csda.2012.05.004
   Web of Science ®Google Scholar
• Cox DR, Hinkley DV. Theoretical statistics. London: Chapman and Hall; 1974.
   Google Scholar
• Efron B. Better bootstrap confidence intervals. J Amer Statist Assoc. 1987;82:171–185. doi: 10.1080/01621459.1987.10478410
   Web of Science ®Google Scholar
• Hall P. Theoretical comparison of bootstrap confidence intervals. Ann Statist. 1988;16:927–953. doi: 10.1214/aos/1176350933
   Web of Science ®Google Scholar
• Efron B, Tibshirani R. An introduction to the bootstrap. New York: Chapman and Hall; 1993.
   Google Scholar
• Borges P, Rodrigues J, Louzada F, et al. A cure rate survival model under a hybrid latent activation scheme. Stat Methods Med Res. 2016;25(2):838–856. doi: 10.1177/0962280212469682
   PubMed Web of Science ®Google Scholar
• Mascarello KC, Zandonade E, Amorim MHC. Survival analysis of women with cervical cancer treated at a referral hospital for oncology in Espírito Santo State, Brazil, 2000–2005. Caderno de Saúde Pública. 2013;4(29):823–831. doi: 10.1590/S0102-311X2013000800019
   Google Scholar