IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p424-d1578505.html
   My bibliography  Save this article

Analysis of Receiver Operating Characteristic Curves for Cure Survival Data and Mismeasured Biomarkers

Author

Listed:
  • Li-Pang Chen

    (Department of Statistics, National Chengchi University, Taipei City 116, Taiwan)

Abstract

Cure models and receiver operating characteristic (ROC) curve estimation are two important issues in survival analysis and have received attention for many years. In the development of biostatistics, these two topics have been well discussed separately. However, a rare development in the estimation of the ROC curve has been made available based on survival data with the cure fraction. On the other hand, while a large body of estimation methods have been proposed, they rely on an implicit assumption that the variables are precisely measured. In applications, measurement errors are generally ubiquitous and ignoring measurement errors can cause unexpected bias for the estimator and lead to the wrong conclusion. In this paper, we study the estimation of the ROC curve and the area under curve (AUC) when variables or biomarkers are subject to measurement error. We propose a valid procedure to handle measurement error effects and estimate the parameters in the cure model, as well as the AUC. We also make an effort to establish the theoretical properties with rigorous justification.

Suggested Citation

  • Li-Pang Chen, 2025. "Analysis of Receiver Operating Characteristic Curves for Cure Survival Data and Mismeasured Biomarkers," Mathematics, MDPI, vol. 13(3), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:424-:d:1578505
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/424/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/424/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Amico, Mailis & Van Keilegom, Ingrid & Legrand, Catherine, 2019. "The Single-Index/Cox Mixture Cure Model," LIDAM Reprints ISBA 2019007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    3. Aurelie Bertrand & Catherine Legrand & Raymond J. Carroll & Christophe de Meester & Ingrid Van Keilegom, 2017. "Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach," Biometrika, Biometrika Trust, vol. 104(1), pages 31-50.
    4. Chen, Li-Pang, 2019. "Semiparametric estimation for cure survival model with left-truncated and right-censored data and covariate measurement error," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    5. Bertrand, Aurelie & Legrand, Catherine & Carroll, Raymond J. & de Meester de Ravenstein, Christophe & Van Keilegom, Ingrid, 2017. "Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach," LIDAM Reprints ISBA 2017046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Jane Paik Kim & Wenbin Lu & Tony Sit & Zhiliang Ying, 2013. "A Unified Approach to Semiparametric Transformation Models Under General Biased Sampling Schemes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 217-227, March.
    7. 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.
    8. 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.
    9. Maïlis Amico & Ingrid Van Keilegom & Catherine Legrand, 2019. "The single‐index/Cox mixture cure model," Biometrics, The International Biometric Society, vol. 75(2), pages 452-462, June.
    10. David Hunter & Kenneth Lange, 2002. "Computing Estimates in the Proportional Odds Model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 155-168, March.
    11. Ma, Yanyuan & Yin, Guosheng, 2008. "Cure Rate Model With Mismeasured Covariates Under Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 743-756, June.
    Full references (including those not matched with items on IDEAS)

    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. Li-Hsiang Lin & Li-Shan Huang, 2024. "Promotion Time Cure Model with Local Polynomial Estimation," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 824-853, December.
    2. Chen, Li-Pang, 2019. "Semiparametric estimation for cure survival model with left-truncated and right-censored data and covariate measurement error," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Bertrand, A. & Legrand, C. & Léonard, D. & Van Keilegom, I., 2017. "Robustness of estimation methods in a survival cure model with mismeasured covariates," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 3-18.
    4. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    5. 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.
    6. Li, Shuwei & Hu, Tao & Zhao, Xingqiu & Sun, Jianguo, 2019. "A class of semiparametric transformation cure models for interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 153-165.
    7. 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).
    8. Ana Ezquerro & Brais Cancela & Ana López-Cheda, 2023. "On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility," Mathematics, MDPI, vol. 11(19), pages 1-21, October.
    9. 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.
    10. 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.
    11. 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.
    12. Sandip Barui & Grace Y. Yi, 2020. "Semiparametric methods for survival data with measurement error under additive hazards cure rate models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 421-450, July.
    13. 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.
    14. Chyong-Mei Chen & Pao-sheng Shen & Yi Liu, 2021. "On semiparametric transformation model with LTRC data: pseudo likelihood approach," Statistical Papers, Springer, vol. 62(1), pages 3-30, February.
    15. Zhang, Ping & Serban, Nicoleta, 2007. "Discovery, visualization and performance analysis of enterprise workflow," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2670-2687, February.
    16. 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.
    17. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    18. 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.
    19. Li Li & Yu Lu & Miaojuan Peng, 2022. "Deterioration Model for Reinforced Concrete Bridge Girders Based on Survival Analysis," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    20. 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.

    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:jmathe:v:13:y:2025:i:3:p:424-:d:1578505. 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.