IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v25y2019i3d10.1007_s10985-018-9450-7.html
   My bibliography  Save this article

What price semiparametric Cox regression?

Author

Listed:
  • Martin Jullum

    (University of Oslo)

  • Nils Lid Hjort

    (University of Oslo)

Abstract

Cox’s proportional hazards regression model is the standard method for modelling censored life-time data with covariates. In its standard form, this method relies on a semiparametric proportional hazards structure, leaving the baseline unspecified. Naturally, specifying a parametric model also for the baseline hazard, leading to fully parametric Cox models, will be more efficient when the parametric model is correct, or close to correct. The aim of this paper is two-fold. (a) We compare parametric and semiparametric models in terms of their asymptotic relative efficiencies when estimating different quantities. We find that for some quantities the gain of restricting the model space is substantial, while it is negligible for others. (b) To deal with such selection in practice we develop certain focused and averaged focused information criteria (FIC and AFIC). These aim at selecting the most appropriate proportional hazards models for given purposes. Our methodology applies also to the simpler case without covariates, when comparing Kaplan–Meier and Nelson–Aalen estimators to parametric counterparts. Applications to real data are also provided, along with analyses of theoretical behavioural aspects of our methods.

Suggested Citation

  • Martin Jullum & Nils Lid Hjort, 2019. "What price semiparametric Cox regression?," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 406-438, July.
  • Handle: RePEc:spr:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-9450-7
    DOI: 10.1007/s10985-018-9450-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-018-9450-7
    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/s10985-018-9450-7?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. Hjort, Nils Lid & Claeskens, Gerda, 2006. "Focused Information Criteria and Model Averaging for the Cox Hazard Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1449-1464, December.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    3. Paul Meier & Theodore Karrison & Rick Chappell & Hui Xie, 2004. "The Price of Kaplan-Meier," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 890-896, January.
    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. Nils Lid Hjort & Emil Aas Stoltenberg, 2023. "The partly parametric and partly nonparametric additive risk model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 372-402, April.
    2. Szilárd Nemes & Erik Bülow & Andreas Gustavsson, 2020. "A Brief Overview of Restricted Mean Survival Time Estimators and Associated Variances," Stats, MDPI, vol. 3(2), pages 1-13, May.
    3. Céline Cunen & Nils Lid Hjort, 2020. "Confidence Distributions for FIC Scores," Econometrics, MDPI, vol. 8(3), pages 1-28, July.

    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. Hai Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    2. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
    3. Céline Cunen & Nils Lid Hjort, 2020. "Confidence Distributions for FIC Scores," Econometrics, MDPI, vol. 8(3), pages 1-28, July.
    4. Guozhi Hu & Weihu Cheng & Jie Zeng, 2023. "Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    5. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    6. Haiying Wang & Yang Li & Jianguo Sun, 2015. "Focused and Model Average Estimation for Regression Analysis of Panel Count Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 732-745, September.
    7. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    8. Jeffrey S. Racine & Qi Li & Dalei Yu & Li Zheng, 2023. "Optimal Model Averaging of Mixed-Data Kernel-Weighted Spline Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1251-1261, October.
    9. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    10. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    11. David Giles, 2007. "Survival of the hippest: life at the top of the hot 100," Applied Economics, Taylor & Francis Journals, vol. 39(15), pages 1877-1887.
    12. Fabio Canova & Christian Matthes, 2021. "Dealing with misspecification in structural macroeconometric models," Quantitative Economics, Econometric Society, vol. 12(2), pages 313-350, May.
    13. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    14. Zhongqi Liang & Qihua Wang & Yuting Wei, 2022. "Robust model selection with covariables missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 539-557, June.
    15. HAEDO, Christian & MOUCHART , Michel & ,, 2013. "Specialized agglomerations with areal data: model and detection," LIDAM Discussion Papers CORE 2013060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    17. Schomaker Michael & Heumann Christian, 2011. "Model Averaging in Factor Analysis: An Analysis of Olympic Decathlon Data," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(1), pages 1-15, January.
    18. 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.
    19. Tumala, Mohammed M & Olubusoye, Olusanya E & Yaaba, Baba N & Yaya, OlaOluwa S & Akanbi, Olawale B, 2017. "Forecasting Nigerian Inflation using Model Averaging methods: Modelling Frameworks to Central Banks," MPRA Paper 88754, University Library of Munich, Germany, revised Feb 2018.
    20. José Manuel Cordero Ferrera & Manuel Muñiz Pérez & Rosa Simancas Rodríguez, 2015. "The influence of socioeconomic factors on cognitive and non-cognitive educational outcomes," Investigaciones de Economía de la Educación volume 10, in: Marta Rahona López & Jennifer Graves (ed.), Investigaciones de Economía de la Educación 10, edition 1, volume 10, chapter 21, pages 413-438, Asociación de Economía de la Educación.

    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:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-9450-7. 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.