IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i2d10.1007_s00180-022-01252-1.html
   My bibliography  Save this article

A linear spline Cox cure model with its applications

Author

Listed:
  • Yu Liu

    (University of California Davis)

  • Chin-Shang Li

    (University at Buffalo)

Abstract

A mixture cure model has been increasingly popular in the field of biostatistics, where some individuals may never experience an event of interest during a study. In most cases, effects of continuous covariates are assumed to be linear. However, a traditional linear assumption often fails in practical situations because real-life effects are usually nonlinear. Proposed is a linear spline Cox cure model in which a spline is used to approximate the unknown smooth functional form for the effect of a continuous covariate to identify the nonlinear functional relationship. The justification and estimation procedure starts from Laplace’s approximation of the marginal log-likelihood function and leads to a penalized log-likelihood. The expectation-maximization algorithm is used to estimate the model parameters, and the proposed methodology could then be used to assess the linearity of the continuous covariate effect via the likelihood ratio procedure. An extensive simulation study is conducted to investigate the performance of the proposed lack-of-fit test for the linearity of the continuous covariate effect. The practical use of the methodology is illustrated with fibrous histiocytoma data from the Surveillance, Epidemiology, and End Results (SEER) program database.

Suggested Citation

  • Yu Liu & Chin-Shang Li, 2023. "A linear spline Cox cure model with its applications," Computational Statistics, Springer, vol. 38(2), pages 935-954, June.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01252-1
    DOI: 10.1007/s00180-022-01252-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01252-1
    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/s00180-022-01252-1?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. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Yingwei Peng & Jeremy M. G. Taylor, 2017. "Residual-based model diagnosis methods for mixture cure models," Biometrics, The International Biometric Society, vol. 73(2), pages 495-505, June.
    3. Wolfgang Härdle & Oliver Linton & Wang & Qihua, 2003. "Semiparametric regression analysis with missing response at random," CeMMAP working papers 11/03, Institute for Fiscal Studies.
    4. Samuli Ripatti & Juni Palmgren, 2000. "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, The International Biometric Society, vol. 56(4), pages 1016-1022, December.
    5. 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.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    7. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    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. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    2. Kalogridis, Ioannis & Van Aelst, Stefan, 2023. "Robust penalized estimators for functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    3. Morteza Amini & Mahdi Roozbeh & Nur Anisah Mohamed, 2024. "Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    4. Shirun Shen & Huiya Zhou & Kejun He & Lan Zhou, 2024. "Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 601-620, September.
    5. Mark J. Meyer & Haobo Cheng & Katherine Hobbs Knutson, 2023. "Bayesian Analysis of Multivariate Matched Proportions with Sparse Response," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 490-509, July.
    6. Giancarlo Aquila & Lucas Barros Scianni Morais & Victor Augusto Durães de Faria & José Wanderley Marangon Lima & Luana Medeiros Marangon Lima & Anderson Rodrigo de Queiroz, 2023. "An Overview of Short-Term Load Forecasting for Electricity Systems Operational Planning: Machine Learning Methods and the Brazilian Experience," Energies, MDPI, vol. 16(21), pages 1-35, November.
    7. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    8. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
    9. Zanin, Luca, 2023. "A flexible estimation of sectoral portfolio exposure to climate transition risks in the European stock market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 39(C).
    10. Gao, Lisa & Shi, Peng, 2022. "Leveraging high-resolution weather information to predict hail damage claims: A spatial point process for replicated point patterns," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 161-179.
    11. Lore Dirick & Gerda Claeskens & Bart Baesens, 2017. "Time to default in credit scoring using survival analysis: a benchmark study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 652-665, June.
    12. Sun, Shilin & Li, Qi & Hu, Wenyang & Liang, Zhongchao & Wang, Tianyang & Chu, Fulei, 2023. "Wind turbine blade breakage detection based on environment-adapted contrastive learning," Renewable Energy, Elsevier, vol. 219(P2).
    13. Caldeira, João F. & Santos, André A.P. & Torrent, Hudson S., 2023. "Semiparametric portfolios: Improving portfolio performance by exploiting non-linearities in firm characteristics," Economic Modelling, Elsevier, vol. 122(C).
    14. Andreas Groll & Trevor Hastie & Gerhard Tutz, 2017. "Selection of effects in Cox frailty models by regularization methods," Biometrics, The International Biometric Society, vol. 73(3), pages 846-856, September.
    15. Waleed B. Altukhaes & Mahdi Roozbeh & Nur A. Mohamed, 2024. "Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    16. Benjamin Owusu & Bettina Bökemeier & Alfred Greiner, 2023. "Assessing nonlinearities and heterogeneity in debt sustainability analysis: a panel spline approach," Empirical Economics, Springer, vol. 64(3), pages 1315-1346, March.
    17. Lu, Steven Qiang & Singh, Sonika & de Roos, Nicolas, 2023. "Effects of online and offline advertising and their synergy on direct telephone sales," Journal of Retailing, Elsevier, vol. 99(3), pages 337-352.
    18. Hamdy F. F. Mahmoud & Inyoung Kim, 2023. "Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    19. Guo, Mengmeng & Zhou, Lhan & Huang, Jianhua Z. & Härdle, Wolfgang Karl, 2013. "Functional data analysis of generalized quantile regressions," SFB 649 Discussion Papers 2013-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. Maximilian Osterhaus, 2024. "A Sparse Grid Approach for the Nonparametric Estimation of High-Dimensional Random Coefficient Models," Papers 2408.07185, arXiv.org.

    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:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01252-1. 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.