International Journal of Cancer Management

Published by: Kowsar

Application of a Mixture Cure Fraction Model Based on the Generalized Modified Weibull Distribution for Analyzing Survival of Patients with Breast Cancer

Parisa Naseri 1 , Ahmad Reza Baghestani 1 , Narges Momenyan 2 , * and Mohammad Esmaeil Akbari 3
Authors Information
1 Department of Biostatistics, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran
2 Department of Medical Informatics, Tarbiat Modares University, Tehran, IR Iran
3 Cancer Research Center, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran
Article information
  • International Journal of Cancer Management: May 2018, 11 (5); e62863
  • Published Online: May 14, 2018
  • Article Type: Research Article
  • Received: October 20, 2017
  • Revised: February 17, 2018
  • Accepted: February 22, 2018
  • DOI: 10.5812/ijcm.62863

To Cite: Naseri P, Baghestani A R, Momenyan N, Esmaeil Akbari M. Application of a Mixture Cure Fraction Model Based on the Generalized Modified Weibull Distribution for Analyzing Survival of Patients with Breast Cancer, Int J Cancer Manag. 2018 ; 11(5):e62863. doi: 10.5812/ijcm.62863.

Copyright © 2018, Cancer Research Center (CRC), Shahid Beheshti University of Medical Sciences. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License ( which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited
1. Background
2. Methods
3. Results
4. Discussion
5. Conclusions
  • 1. Garcia-Laencina PJ, Abreu PH, Abreu MH, Afonoso N. Missing data imputation on the 5-year survival prediction of breast cancer patients with unknown discrete values. Comput Biol Med. 2015;59:125-33. doi: 10.1016/j.compbiomed.2015.02.006. [PubMed: 25725446].
  • 2. Grau AM, Ata A, Foster L, Ahmed NU, Gorman DR, Shyr Y, et al. Effect of race on long-term survival of breast cancer patients: transinstitutional analysis from an inner city hospital and university medical center. Am Surg. 2005;71(2):164-70. [PubMed: 16022018].
  • 3. Foo CS, Su D, Chong CK, Chng HC, Tay KH, Low SC, et al. Breast cancer in young Asian women: study on survival. ANZ J Surg. 2005;75(7):566-72. doi: 10.1111/j.1445-2197.2005.03431.x. [PubMed: 15972049].
  • 4. Baghestani AR, Moghaddam SS, Majd HA, Akbari ME, Nafissi N, Gohari K. Application of a Non-Mixture Cure Rate Model for Analyzing Survival of Patients with Breast Cancer. Asian Pac J Cancer Prev. 2015;16(16):7359-63. [PubMed: 26514537].
  • 5. Momenyan S, Baghestani AR, Momenyan N, Naseri P, et al. Survival prediction of patients with breast cancer: comparisons of decision tree and logistic regression analysis. Int J Cancer Manag. 2018. Forthcoming. e9176.
  • 6. Haghshenas MR, Mousavi T, Moosazadeh M, Afshari M. Human papillomavirus and breast cancer in Iran: a meta- analysis. Iran J Basic Med Sci. 2016;19(3):231-7. [PubMed: 27114791]. [PubMed Central: PMC4834111].
  • 7. Bundred NJ. Prognostic and predictive factors in breast cancer. Cancer Treat Rev. 2001;27(3):137-42. doi: 10.1053/ctrv.2000.0207. [PubMed: 11417963].
  • 8. Ture M, Tokatli F, Kurt I. Using Kaplan–Meier analysis together with decision tree methods (C&RT, CHAID, QUEST, C4.5 and ID3) in determining recurrence-free survival of breast cancer patients. Expert Systems Appl. 2009;36(2):2017-26. doi: 10.1016/j.eswa.2007.12.002.
  • 9. Davoodi SH, Malek-Shahabi T, Malekshahi-Moghadam A, Shahbazi R, Esmaeili S. Obesity as an important risk factor for certain types of cancer. Iran J Cancer Prev. 2013;6(4):186-94. [PubMed: 25250133]. [PubMed Central: PMC4142931].
  • 10. Delen D, Walker G, Kadam A. Predicting breast cancer survivability: a comparison of three data mining methods. Artif Intell Med. 2005;34(2):113-27. doi: 10.1016/j.artmed.2004.07.002. [PubMed: 15894176].
  • 11. Lambert PC. Modeling of the cure fraction in survival studies. Stata J. 2007;7(3):351.
  • 12. Lambert PC, Thompson JR, Weston CL, Dickman PW. Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics. 2007;8(3):576-94. doi: 10.1093/biostatistics/kxl030. [PubMed: 17021277].
  • 13. Gu Y, Sinha D, Banerjee S. Analysis of cure rate survival data under proportional odds model. Lifetime Data Anal. 2011;17(1):123-34. doi: 10.1007/s10985-010-9171-z. [PubMed: 20521166]. [PubMed Central: PMC2943572].
  • 14. Arano I, Sugimoto T, Hamasaki T, Ohno Y. Practical application of cure mixture model for long-term censored survivor data from a withdrawal clinical trial of patients with major depressive disorder. BMC Med Res Methodol. 2010;10:33. doi: 10.1186/1471-2288-10-33. [PubMed: 20412598]. [PubMed Central: PMC2880122].
  • 15. Peto R, Lee PN, Paige WS. Statistical analysis of the bioassay of continuous carcinogens. Br J Cancer. 1972;26(4):258-61. [PubMed: 5071187]. [PubMed Central: PMC2008655].
  • 16. Carrasco JMF, Ortega EMM, Cordeiro GM. A generalized modified Weibull distribution for lifetime modeling. Comput Statistics Data Analysis. 2008;53(2):450-62. doi: 10.1016/j.csda.2008.08.023.
  • 17. Wang D. Maller RA, Zhou X, Survival analysis with long-term survivors. Statistic Methods Med Res. 2000;9:520.
  • 18. Abu Bakar MR, Salah KA, Ibrahim NA. Cure fraction, modelling and estimating in a population-based cancer survival analysis. Malaysian J Math Sci. 2008;2:113-34.
  • 19. Asano J, Hirakawa A, Hamada C. Assessing the prediction accuracy of cure in the Cox proportional hazards cure model: an application to breast cancer data. Pharm Stat. 2014;13(6):357-63. doi: 10.1002/pst.1630. [PubMed: 25044997].
  • 20. Ortega EMM, Barriga GDC, Hashimoto EM, Cancho VG, Cordeiro GM. A new class of survival regression models with cure fraction. J Data Sci. 2014;12(1):107-36.
  • 21. Bradburn MJ, Clark TG, Love SB, Altman DG. Survival analysis part II: multivariate data analysis--an introduction to concepts and methods. Br J Cancer. 2003;89(3):431-6. doi: 10.1038/sj.bjc.6601119. [PubMed: 12888808]. [PubMed Central: PMC2394368].
  • 22. Cox PR. Life Tables. Wiley Online Library; 1972.
  • 23. Kuk AYC, Chen CH. A mixture model combining logistic regression with proportional hazards regression. Biometrika. 1992;79(3):531-41.
  • 24. Sy JP, Taylor JM. Estimation in a Cox proportional hazards cure model. Biometrics. 2000;56(1):227-36. [PubMed: 10783800].
  • 25. Lu W. Maximum likelihood estimation in the proportional hazards cure model. Ann Inst Statistic Math. 2007;60(3):545-74. doi: 10.1007/s10463-007-0120-x.
  • 26. Rama R, Swaminathan R, Venkatesan P. Cure models for estimating hospital-based breast cancer survival. Asian Pac J Cancer Prev. 2010;11(2):387-91. [PubMed: 20843121].
  • 27. Achcar JA, Coelho-Barros EA, Mazucheli J. Cure fraction models using mixture and non-mixture models. Tatra Mountains Math Publicat. 2012;51(1):1-9. doi: 10.2478/v10127-012-0001-4.
  • 28. Othus M, Barlogie B, Leblanc ML, Crowley JJ. Cure models as a useful statistical tool for analyzing survival. Clin Cancer Res. 2012;18(14):3731-6. doi: 10.1158/1078-0432.CCR-11-2859. [PubMed: 22675175]. [PubMed Central: PMC3744099].
  • 29. Akhlaghi AA, Najafi I, Mahmoodi M, Shojaee A, Yousefifard M, Hosseini M. Survival analysis of Iranian patients undergoing continuous ambulatory peritoneal dialysis using cure model. J Res Health Sci. 2013;13(1):32-6. [PubMed: 23772014].
  • 30. Yu XQ, De Angelis R, Andersson TM, Lambert PC, O'Connell DL, Dickman PW. Estimating the proportion cured of cancer: some practical advice for users. Cancer Epidemiol. 2013;37(6):836-42. doi: 10.1016/j.canep.2013.08.014. [PubMed: 24042025].
  • 31. Rahimzadeh M, Baghestani AR, Gohari MR, Pourhoseingholi MA. Estimation of the cure rate in Iranian breast cancer patients. Asian Pac J Cancer Prev. 2014;15(12):4839-42. [PubMed: 24998549].
  • 32. Ture M, Tokatli F, Kurt Omurlu I. The comparisons of prognostic indexes using data mining techniques and Cox regression analysis in the breast cancer data. Expert Systems Applicat. 2009;36(4):8247-54. doi: 10.1016/j.eswa.2008.10.014.
  • 33. Abadi A, Yavari P, Dehghani-Arani M, Alavi-Majd H, Ghasemi E, Amanpour F, et al. Cox models survival analysis based on breast cancer treatments. Iran J Cancer Prev. 2014;7(3):124-9. [PubMed: 25250162]. [PubMed Central: PMC4171826].
  • 34. Rezaianzadeh A, Peacock J, Reidpath D, Talei A, Hosseini SV, Mehrabani D. Survival analysis of 1148 women diagnosed with breast cancer in Southern Iran. BMC Cancer. 2009;9:168. doi: 10.1186/1471-2407-9-168. [PubMed: 19497131]. [PubMed Central: PMC2699348].
  • 35. Kuru B, Camlibel M, Gulcelik MA, Alagol H. Prognostic factors affecting survival and disease-free survival in lymph node-negative breast carcinomas. J Surg Oncol. 2003;83(3):167-72. doi: 10.1002/jso.10264. [PubMed: 12827686].
  • 36. Arpino G, Bardou VJ, Clark GM, Elledge RM. Infiltrating lobular carcinoma of the breast: tumor characteristics and clinical outcome. Breast Cancer Res. 2004;6(3):R149-56. doi: 10.1186/bcr767. [PubMed: 15084238]. [PubMed Central: PMC400666].
  • 37. Ziaei JE, Sanaat Z, Asvadi I, Dastgiri S, Pourzand A, Vaez J. Survival analysis of breast cancer patients in northwest Iran. Asian Pac J Cancer Prev. 2013;14(1):39-42. [PubMed: 23534759].
  • 38. Vahdaninia M, Montazeri A. Breast cancer in Iran: a survival analysis. Asian Pac J Cancer Prev. 2004;5(2):223-5. [PubMed: 15244529].
  • 39. Akbari A, Razzaghi Z, Homaee F, Khayamzadeh M, Movahedi M, Akbari ME. Parity and breastfeeding are preventive measures against breast cancer in Iranian women. Breast Cancer. 2011;18(1):51-5. doi: 10.1007/s12282-010-0203-z. [PubMed: 20217489].
  • 40. Akbari ME, Khayamzadeh M, Khoshnevis SJ, Nafisi N, Akbari A. Five and ten years survival in breast cancer patients mastectomies vs. breast conserving surgeries personal experience. Iran J Cancer Prevent. 2008;1(2):53-6.
  • 41. Faradmal J, Talebi A, Rezaianzadeh A, Mahjub H. Survival analysis of breast cancer patients using Cox and frailty models. J Res Health Sci. 2012;12(2):127-30. [PubMed: 23241526].
  • 42. Nafissi N, Saghafinia M, Motamedi MH, Akbari ME. A survey of breast cancer knowledge and attitude in Iranian women. J Cancer Res Ther. 2012;8(1):46-9. doi: 10.4103/0973-1482.95173. [PubMed: 22531513].
  • 43. Movahedi M, Haghighat S, Khayamzadeh M, Moradi A, Ghanbari-Motlagh A, Mirzaei H, et al. Survival rate of breast cancer based on geographical variation in iran, a national study. Iran Red Crescent Med J. 2012;14(12):798-804. doi: 10.5812/ircmj.3631. [PubMed: 23483369]. [PubMed Central: PMC3587870].
  • 44. Jafari-Koshki T, Mansourian M, Mokarian F. Exploring factors related to metastasis free survival in breast cancer patients using Bayesian cure models. Asian Pac J Cancer Prev. 2014;15(22):9673-8. [PubMed: 25520087].
  • 45. Momenyan S, Sadeghifar M, Sarvi F, Khodadost M, Mosavi-Jarrahi A, Ghaffari ME, et al. Relationship between Urbanization and Cancer Incidence in Iran Using Quantile Regression. Asian Pac J Cancer Prev. 2016;17(S3):113-7. [PubMed: 27165247].
  • 46. Peng Y, Dear KB, Denham JW. A generalized F mixture model for cure rate estimation. Stat Med. 1998;17(8):813-30. [PubMed: 9595613].
  • 47. Yamaguchi K. Accelerated Failure-Time Regression Models with a Regression Model of Surviving Fraction: An Application to the Analysis of "Permanent Employment" in Japan. J Am Statistic Assoc. 1992;87(418):284. doi: 10.2307/2290258.
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