IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v31y2004i1p43-50.html

An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions

Author

Listed:
  • Thomas Augustin

Abstract

. This paper studies Cox's proportional hazards model under covariate measurement error. Nakamura's [Biometrika 77 (1990) 127] methodology of corrected log‐likelihood will be applied to the so‐called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non‐normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura [Biometrics 48 (1992) 829], Kong et al. [Scand. J. Statist. 25 (1998) 573] and Kong & Gu [Statistica Sinica 9 (1999) 953] are re‐established in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.

Suggested Citation

  • Thomas Augustin, 2004. "An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 43-50, March.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:43-50
    DOI: 10.1111/j.1467-9469.2004.00371.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2004.00371.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2004.00371.x?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
    ---><---

    References listed on IDEAS

    as
    1. Christopher J. Flinn & James J. Heckman, 1982. "Models for the Analysis of Labor Force Dynamics," NBER Working Papers 0857, National Bureau of Economic Research, Inc.
    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. Liang Li & Bo Hu & Tom Greene, 2009. "A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study," Biometrics, The International Biometric Society, vol. 65(3), pages 737-745, September.
    2. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    3. Hans Schneeweiss & Thomas Augustin, 2006. "Some recent advances in measurement error models and methods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 183-197, March.
    4. Muff, Stefanie & Ott, Manuela & Braun, Julia & Held, Leonhard, 2017. "Bayesian two-component measurement error modelling for survival analysis using INLA—A case study on cardiovascular disease mortality in Switzerland," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 177-193.
    5. Buzas, Jeffrey S., 2009. "A note on corrected scores for logistic regression," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2351-2358, November.
    6. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
    7. Yanlin Tang & Xinyuan Song & Grace Yun Yi, 2022. "Bayesian analysis under accelerated failure time models with error-prone time-to-event outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 139-168, January.
    8. Li-Pang Chen & Grace Y. Yi, 2021. "Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 481-517, 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. Rendon Sílvio, 2006. "Job Search And Asset Accumulation Under Borrowing Constraints ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(1), pages 233-263, February.
    2. Lisa M. Lynch, 1986. "The Youth Labor Market in the 80s: Determinants of Re-Employment Probabilities for Young Men and Women," NBER Working Papers 2021, National Bureau of Economic Research, Inc.
    3. Furuya, Kaku, 2002. "A socio-economic model of stigma and related social problems," Journal of Economic Behavior & Organization, Elsevier, vol. 48(3), pages 281-290, July.
    4. Jones, Stephen R G & Riddell, W Craig, 1995. "The Measurement of Labor Force Dynamics with Longitudinal Data: The Labour Market Activity Survey Filter," Journal of Labor Economics, University of Chicago Press, vol. 13(2), pages 351-385, April.
    5. Bart Cockx & Matteo Picchio, 2013. "Scarring effects of remaining unemployed for long-term unemployed school-leavers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(4), pages 951-980, October.
    6. Lawrence F. Katz, 1986. "Layoffs, Recall and the Duration of Unemployment," NBER Working Papers 1825, National Bureau of Economic Research, Inc.
    7. Agarwal, Sumit & Ambrose, Brent W. & Chomsisengphet, Souphala & Liu, Chunlin, 2006. "An empirical analysis of home equity loan and line performance," Journal of Financial Intermediation, Elsevier, vol. 15(4), pages 444-469, October.
    8. Sumit Agarwal & Souphala Chomsisengphet & Lawrence Mielnicki, 2008. "Do Forbearance Plans Help Mitigate Credit Card Losses?," Journal of Family and Economic Issues, Springer, vol. 29(2), pages 191-201, June.
    9. Amelie Constant & Klaus F. Zimmermann, 2004. "Self-Employment Dynamics across the Business Cycle: Migrants versus Natives," Discussion Papers of DIW Berlin 455, DIW Berlin, German Institute for Economic Research.
    10. Boheim, Rene & Taylor, Mark P., 2002. "The search for success: do the unemployed find stable employment?," Labour Economics, Elsevier, vol. 9(6), pages 717-735, December.
    11. Jonathan Lee & Peter Boatwright & Wagner A. Kamakura, 2003. "A Bayesian Model for Prelaunch Sales Forecasting of Recorded Music," Management Science, INFORMS, vol. 49(2), pages 179-196, February.
    12. Meta Brown & Christopher J. Flinn & Joseph Mullins, 2025. "Family Law Effects on Divorce, Fertility, and Child Investment," Journal of Labor Economics, University of Chicago Press, vol. 43(S1), pages 351-397.
    13. Thomas, Jonathan M, 1996. "An Empirical Model of Sectoral Movements by Unemployed Workers," Journal of Labor Economics, University of Chicago Press, vol. 14(1), pages 126-153, January.
    14. Gagliarducci, Stefano, 2005. "The dynamics of repeated temporary jobs," Labour Economics, Elsevier, vol. 12(4), pages 429-448, August.
    15. Tracy, Joseph S, 1987. "An Empirical Test of an Asymmetric Information Model of Strikes," Journal of Labor Economics, University of Chicago Press, vol. 5(2), pages 149-173, April.
    16. B. P. S. Murthi & Sumit Sarkar, 2003. "The Role of the Management Sciences in Research on Personalization," Management Science, INFORMS, vol. 49(10), pages 1344-1362, October.
    17. Bloemen, Hans G., 1997. "Job search theory, labour supply and unemployment duration," Journal of Econometrics, Elsevier, vol. 79(2), pages 305-325, August.
    18. Hans Schneeweiss & Thomas Augustin, 2006. "Some recent advances in measurement error models and methods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 183-197, March.
    19. Carolina Fugazza, 2018. "Anatomy of Unemployment Risk," Working papers 048, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    20. Ondrich, Jan & Rhody, Stephen E., 1999. "Multiple spells in the Prentice-Gloeckler-Meyer likelihood with unobserved heterogeneity," Economics Letters, Elsevier, vol. 63(2), pages 139-144, May.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:31:y:2004:i:1:p:43-50. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.