IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v1y2018i1p13-188d183187.html
   My bibliography  Save this article

A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution

Author

Listed:
  • Durga H. Kutal

    (Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
    Durga H. Kutal currently is a visiting assistant professor at Wake Forest University, NC, USA.)

  • Lianfen Qian

    (Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
    Lianfen Qian is a distinguished guest professor of Wenzhou University, Wenzhou, China.)

Abstract

This paper considers a non-mixture cure model for right-censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Compared with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

Suggested Citation

  • Durga H. Kutal & Lianfen Qian, 2018. "A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution," Stats, MDPI, vol. 1(1), pages 1-13, November.
    • Handle: RePEc:gam:jstats:v:1:y:2018:i:1:p:13-188:d:183187
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/1/1/13/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/1/1/13/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Patilea, Valentin & Van Keilegom, Ingrid, 2017. "A general approach for cure models in survival analysis," LIDAM Discussion Papers ISBA 2017008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    3. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    4. Joseph G. Ibrahim & Ming-Hui Chen & Debajyoti Sinha, 2001. "Bayesian Semiparametric Models for Survival Data with a Cure Fraction," Biometrics, The International Biometric Society, vol. 57(2), pages 383-388, June.
    5. Liu, Hao & Shen, Yu, 2009. "A Semiparametric Regression Cure Model for Interval-Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1168-1178.
    6. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    7. Els Goetghebeur & Louise Ryan, 2000. "Semiparametric Regression Analysis of Interval-Censored Data," Biometrics, The International Biometric Society, vol. 56(4), pages 1139-1144, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Reza Azimi & Mahdy Esmailian & Diego I. Gallardo & Héctor J. Gómez, 2022. "A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data," Mathematics, MDPI, vol. 10(24), pages 1-17, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohamed Elamin Abdallah Mohamed Elamin Omer & Mohd Rizam Abu Bakar & Mohd Bakri Adam & Mohd Shafie Mustafa, 2020. "Cure Models with Exponentiated Weibull Exponential Distribution for the Analysis of Melanoma Patients," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    2. Bremhorst, Vincent & Lambert, Philippe, 2013. "Flexible estimation in cure survival models using Bayesian P-splines," LIDAM Discussion Papers ISBA 2013039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Guoqing Diao & Ao Yuan, 2019. "A class of semiparametric cure models with current status data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 26-51, January.
    4. Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 270-284.
    5. Guosheng Yin, 2005. "Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study," Biometrics, The International Biometric Society, vol. 61(2), pages 552-558, June.
    6. Guosheng Yin & Joseph G. Ibrahim, 2005. "A General Class of Bayesian Survival Models with Zero and Nonzero Cure Fractions," Biometrics, The International Biometric Society, vol. 61(2), pages 403-412, June.
    7. N. Balakrishnan & M. V. Koutras & F. S. Milienos & S. Pal, 2016. "Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 937-966, December.
    8. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    9. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    10. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
    11. Portier, Francois & El Ghouch, Anouar & Van Keilegom, Ingrid, 2015. "Efficiency and Bootstrap in the Promotion Time Cure Model," LIDAM Discussion Papers ISBA 2015012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Han, Bo & Wang, Xiaoguang, 2020. "Semiparametric estimation for the non-mixture cure model in case-cohort and nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    13. Gressani, Oswaldo & Lambert, Philippe, 2016. "Fast Bayesian inference in semi-parametric P-spline cure survival models using Laplace approximations," LIDAM Discussion Papers ISBA 2016041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    15. Amico, Mailis & Van Keilegom, Ingrid, 2017. "Cure models in survival analysis," LIDAM Discussion Papers ISBA 2017007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Gressani, Oswaldo & Lambert, Philippe, 2018. "Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 151-167.
    17. Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    18. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    19. Prabhashi W. Withana Gamage & Monica Chaudari & Christopher S. McMahan & Edwin H. Kim & Michael R. Kosorok, 2020. "An extended proportional hazards model for interval-censored data subject to instantaneous failures," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 158-182, January.
    20. Sangbum Choi & Xuelin Huang, 2012. "A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1126-1135, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:1:y:2018:i:1:p:13-188:d:183187. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.