A Parametric Non-Mixture Cure Survival Model with Censored Data

  • Noor Akma IbrahimEmail author
  • Fauzia Taweab
  • Jayanthi Arasan
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)


In some medical studies, there is often an interest in the number of patients who are not susceptible to the event of interest (recurrence of disease) and expected to be cured. This article investigates the cure rate estimation based on non-mixture cure model in the presence of left, right and interval censored data. The model proposed based on log-normal distribution that incorporates the effects of covariates on the cure probability. The maximum likelihood estimation (MLE) approach is employed to estimate the model parameters and a simulation study is provided for assessing the efficiency of the proposed estimation procedure under various conditions.


Censored data Cure fraction Interval Lognormal distribution MLE method Non-mixture cure model 



The authors are much thankful and grateful to the Institute for Mathematical Research, Universiti Putra Malaysia (UPM), for their generous support of this study.


  1. 1.
    Berkson J, Gage R (1952) Survival curve for cancer patients following treatment. J Amer Statist Assoc 47:501–515Google Scholar
  2. 2.
    Taylor JMG (1995) Semi-parametric estimation in failure time mixture models. Biometrics 51:899–907Google Scholar
  3. 3.
    Maller RA, Zhou X (1996) Survival Analysis with Long-Term Survivors, Chichester. John Wiley and SonsGoogle Scholar
  4. 4.
    Sy JP, Taylor JMG(2000) Estimation in a cox proportional hazards cure model. Biometrics 56:227–236Google Scholar
  5. 5.
    Achcar A, Jorge, Coelho- Barros Emi’lio, A, Josmar Mazuchell (2012) T Cure fraction models using mixture and non-mixture models. Tatra Mt Math Publ 51:1–9Google Scholar
  6. 6.
    Mizoi MF, Bolfarine H, Lima ACP (2007) Cure rate models with measurement errors. Communications in Statistics—Simulation and Computation 36:185–196Google Scholar
  7. 7.
    Chen MH, Ibrahim JG, Sinha DA (1999) A new bayesian model for survival data with a surviving fraction. J Amer Statist Assoc 94:909–9198Google Scholar
  8. 8.
    Tsodikov AD, Ibrahim JG, Yakovlev AY (2003) Estimating cure rates from survival data: an alternative to two-component mixture models. J Amer Statist Assoc 98:1063–1078Google Scholar
  9. 9.
    Banerjee S, Carlin BP J (2004) The Parametric spatial cure rate models for interval-censored time-to-relapse data. Biometrics 60:268–275Google Scholar
  10. 10.
    Liu Hao, Shen (2009) A semi parametric regression cure model for interval censored data. J Amer Statist Assoc 487:1168–1178Google Scholar
  11. 11.
    Gutierrez RG (2002) Parametric frailty and shared frailty survival models. Stata 2:22–44Google Scholar
  12. 12.
    Zeng D, Yin G, Ibrahim JG (2006) Semi parametric transformation models for survival data with a cure fraction. J Amer Statist Assoc 101:670–684Google Scholar
  13. 13.
    Lindsey JC, Ryan LM (1998) Tutorial in biostatistics methods for interval censored data. Stat Med 17:219–238Google Scholar
  14. 14.
    Gomez G, Calle ML, Oller R (2004) Frequentist and bayesian approaches for interval-censored data. Statist Pap 45:139–173Google Scholar
  15. 15.
    Gomez G, Calle ML, Oller R, Langohr K (2009) Tutorial on methods for interval-censored data and their implementation in R. Statist Model 9:259–297Google Scholar
  16. 16.
    Lam KF, Xue H (2005) A semiparametric regression cure model with current status data. Biometrika 92:573–586Google Scholar
  17. 17.
    Kim Y, Jhun M (2008) Cure rate model with interval censored data. Stat Med 27:3–14Google Scholar
  18. 18.
    Sun J (2006) The statistical analysis of interval censored failure time data. Springer, New YorkGoogle Scholar
  19. 19.
    Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, Wiley, New YorkGoogle Scholar
  20. 20.
    Claire L Weston, John R Thompson (2010) Modeling survival in childhood cancer studies using two- stage non-mixture cure models. Journal of Applied Statistics 37:1523–1535Google Scholar
  21. 21.
    Zhao Guolin MA (2008) Nonparametric and Parametric Survival Analysis of Censored Data with Possible Violation of Method Assumptions. Ph.D. Diss, North Carolina UniversityGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Noor Akma Ibrahim
    • 1
    Email author
  • Fauzia Taweab
    • 2
    • 3
  • Jayanthi Arasan
    • 1
  1. 1.Department of MathematicsUniversiti Putra MalaysiaSerdangMalaysia
  2. 2.Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia
  3. 3.Department of StatisticsUniversity of TripoliTripoliLibya

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