IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v29y2020i4d10.1007_s11749-019-00698-8.html
   My bibliography  Save this article

The nonparametric location-scale mixture cure model

Author

Listed:
  • Justin Chown

    (Ruhr-Universität Bochum)

  • Cédric Heuchenne

    (University of Liège
    Université Catholique de Louvain)

  • Ingrid Van Keilegom

    (KU Leuven)

Abstract

We propose completely nonparametric methodology to investigate location-scale modeling of two-component mixture cure models that is similar in spirit to accelerated failure time models, where the responses of interest are only indirectly observable due to the presence of censoring and the presence of long-term survivors that are always censored. We use nonparametric estimators of the location-scale model components that depend on a bandwidth sequence to propose an estimator of the error distribution function that has not been considered before in the literature. When this bandwidth belongs to a certain range of undersmoothing bandwidths, the proposed estimator of the error distribution function is root-n consistent. A simulation study investigates the finite sample properties of our approach, and the methodology is illustrated using data obtained to study the behavior of distant metastasis in lymph-node-negative breast cancer patients.

Suggested Citation

  • Justin Chown & Cédric Heuchenne & Ingrid Van Keilegom, 2020. "The nonparametric location-scale mixture cure model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1008-1028, December.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:4:d:10.1007_s11749-019-00698-8
    DOI: 10.1007/s11749-019-00698-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-019-00698-8
    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/s11749-019-00698-8?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, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, September.
    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    3. 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.
    4. 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.
    5. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    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. Zeng, Donglin & Yin, Guosheng & Ibrahim, Joseph G., 2006. "Semiparametric Transformation Models for Survival Data With a Cure Fraction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 670-684, June.
    8. 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.
    9. Lopez-Cheda, Ana & Cao, Ricardo & Jacome, Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," LIDAM Reprints ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. 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.
    2. Escobar-Bach, Mikael & Van Keilegom, Ingrid, 2023. "Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).

    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. Ana López-Cheda & M. Amalia Jácome & Ricardo Cao, 2017. "Nonparametric latency estimation for mixture cure models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 353-376, June.
    2. 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).
    3. Peláez, Rebeca & Van Keilegom, Ingrid & Cao, Ricardo & Vilar, Juan M., 2024. "Probability of default estimation in credit risk using mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    4. Philippe Lambert & Vincent Bremhorst, 2020. "Inclusion of time‐varying covariates in cure survival models with an application in fertility studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 333-354, January.
    5. 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.
    6. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    7. 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.
    8. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    9. 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).
    10. 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.
    11. 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.
    12. Richard Tawiah & Geoffrey J. McLachlan & Shu Kay Ng, 2020. "A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction," Biometrics, The International Biometric Society, vol. 76(3), pages 753-766, September.
    13. 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.
    14. 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).
    15. Peizhi Li & Yingwei Peng & Ping Jiang & Qingli Dong, 2020. "A support vector machine based semiparametric mixture cure model," Computational Statistics, Springer, vol. 35(3), pages 931-945, September.
    16. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    17. Suvra Pal & Yingwei Peng & Wisdom Aselisewine, 2024. "A new approach to modeling the cure rate in the presence of interval censored data," Computational Statistics, Springer, vol. 39(5), pages 2743-2769, July.
    18. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    19. Muller, Ursula & Van Keilegom, Ingrid, 2016. "Goodness-of-t tests for the cure rate in a mixture cure model," LIDAM Discussion Papers ISBA 2016037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Wenbin Lu, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, 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:29:y:2020:i:4:d:10.1007_s11749-019-00698-8. 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.