IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v32y2023i2d10.1007_s11749-022-00840-z.html
   My bibliography  Save this article

Nonparametric estimation in mixture cure models with covariates

Author

Listed:
  • Ana López-Cheda

    (University of A Coruña)

  • Yingwei Peng

    (Queen’s University)

  • María Amalia Jácome

    (University of A Coruña)

Abstract

Nonparametric estimation methods for the cure rate and the distribution of the failure time of uncured subjects with covariates for censored survival data have attracted much attention in the last few years. To model the effects of covariates on the distribution of the failure time of uncured subjects, existing works assume that the cure rate is a constant or depends on the same covariate as the distribution of uncured subjects. In this paper, we review the nonparametric estimation methods in the context of the mixture cure model and propose a new nonparametric estimator for the distribution of uncured subjects that relaxes the assumption used in the existing works. The estimation is based on the EM algorithm, which is readily available for mixture cure models, and is strongly consistent. The finite sample performance of the proposed estimator is assessed and compared with existing methods in a simulation study. Finally, the nonparametric estimation methods are employed to model the effects of some covariates on the time to bankruptcy among commercial banks insured by the Federal Deposit Insurance Corporation during the first quarter of 2006.

Suggested Citation

  • Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:2:d:10.1007_s11749-022-00840-z
    DOI: 10.1007/s11749-022-00840-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00840-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-022-00840-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    2. Patilea, Valentin & Van Keilegom, Ingrid, 2020. "A general approach for cure models in survival analysis," LIDAM Reprints ISBA 2020042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    4. Beretta, Alessandro & Heuchenne, Cedric, 2019. "Variable selection in proportional hazards cure model with time-varying covariates, application to US bank failures," LIDAM Reprints ISBA 2019018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2012. "Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 790-810, December.
    6. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    7. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    8. Alessandro Beretta & Cédric Heuchenne, 2019. "Variable selection in proportional hazards cure model with time-varying covariates, application to US bank failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(9), pages 1529-1549, July.
    9. Zhang, Jiajia & Peng, Yingwei & Li, Haifen, 2013. "A new semiparametric estimation method for accelerated hazards mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 95-102.
    10. Mao, Meng & Wang, Jane-Ling, 2010. "Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 302-311.
    11. U U Müller & I Van Keilegom, 2019. "Goodness-of-fit tests for the cure rate in a mixture cure model," Biometrika, Biometrika Trust, vol. 106(1), pages 211-227.
    12. Yuanshan Wu & Guosheng Yin, 2017. "Multiple imputation for cure rate quantile regression with censored data," Biometrics, The International Biometric Society, vol. 73(1), pages 94-103, March.
    13. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    14. Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    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. Philippe Lambert, 2023. "Comments on: Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 506-509, June.

    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. 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.
    2. López-Cheda, Ana & Cao, Ricardo & Jácome, M. Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 144-165.
    3. Yuanshan Wu & Guosheng Yin, 2017. "Multiple imputation for cure rate quantile regression with censored data," Biometrics, The International Biometric Society, vol. 73(1), pages 94-103, March.
    4. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    5. 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.
    6. Motahareh Parsa & Ingrid Van Keilegom, 2023. "Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?," Statistical Papers, Springer, vol. 64(3), pages 835-855, June.
    7. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    8. Wende Clarence Safari & Ignacio López-de-Ullibarri & María Amalia Jácome, 2023. "Latency function estimation under the mixture cure model when the cure status is available," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 608-627, July.
    9. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    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. Mengling Liu & Wenbin Lu & Yongzhao Shao, 2006. "Interval Mapping of Quantitative Trait Loci for Time-to-Event Data with the Proportional Hazards Mixture Cure Model," Biometrics, The International Biometric Society, vol. 62(4), pages 1053-1061, December.
    12. 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.
    13. Yi-Hsuan Lee & Zhiliang Ying, 2015. "A Mixture Cure-Rate Model for Responses and Response Times in Time-Limit Tests," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 748-775, September.
    14. 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.
    15. 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.
    16. 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.
    17. Yilong Zhang & Xiaoxia Han & Yongzhao Shao, 2021. "The ROC of Cox proportional hazards cure models with application in cancer studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 195-215, April.
    18. Tomoyuki Sugimoto & Toshimitsu Hamasaki, 2006. "Properties of estimators of baseline hazard functions in a semiparametric cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 647-674, December.
    19. Lopez-Cheda , Ana & Cao, Ricardo & Jacome, Maria Amalia & Van Keilegom, Ingrid, 2015. "Nonparametric incidence and latency estimation in mixture cure models," LIDAM Discussion Papers ISBA 2015014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.

    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:spr:testjl:v:32:y:2023:i:2:d:10.1007_s11749-022-00840-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.