IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v72y2020i4d10.1007_s10463-019-00716-4.html
   My bibliography  Save this article

Large sample results for frequentist multiple imputation for Cox regression with missing covariate data

Author

Listed:
  • Frank Eriksson

    (University of Copenhagen)

  • Torben Martinussen

    (University of Copenhagen)

  • Søren Feodor Nielsen

    (Copenhagen Business School)

Abstract

Incomplete information on explanatory variables is commonly encountered in studies of possibly censored event times. A popular approach to deal with partially observed covariates is multiple imputation, where a number of completed data sets, that can be analyzed by standard complete data methods, are obtained by imputing missing values from an appropriate distribution. We show how the combination of multiple imputations from a compatible model with suitably estimated parameters and the usual Cox regression estimators leads to consistent and asymptotically Gaussian estimators of both the finite-dimensional regression parameter and the infinite-dimensional cumulative baseline hazard parameter. We also derive a consistent estimator of the covariance operator. Simulation studies and an application to a study on survival after treatment for liver cirrhosis show that the estimators perform well with moderate sample sizes and indicate that iterating the multiple-imputation estimator increases the precision.

Suggested Citation

  • Frank Eriksson & Torben Martinussen & Søren Feodor Nielsen, 2020. "Large sample results for frequentist multiple imputation for Cox regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 969-996, August.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00716-4
    DOI: 10.1007/s10463-019-00716-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-019-00716-4
    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/s10463-019-00716-4?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. Chen H.Y., 2002. "Double-Semiparametric Method for Missing Covariates in Cox Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 565-576, June.
    2. Torben Martinussen, 1999. "Cox Regression with Incomplete Covariate Measurements using the EM‐algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 479-491, December.
    3. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, 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. Torben Martinussen & Klaus K. Holst & Thomas H. Scheike, 2016. "Cox regression with missing covariate data using a modified partial likelihood method," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 570-588, October.
    2. Yanyao Yi & Ting Ye & Menggang Yu & Jun Shao, 2020. "Cox regression with survival‐time‐dependent missing covariate values," Biometrics, The International Biometric Society, vol. 76(2), pages 460-471, June.
    3. X. Hu & Bin Zhang, 2012. "Pseudolikelihood ratio test with biased observations," Statistical Papers, Springer, vol. 53(2), pages 387-400, May.
    4. Jon Arni Steingrimsson & Robert L. Strawderman, 2017. "Estimation in the Semiparametric Accelerated Failure Time Model With Missing Covariates: Improving Efficiency Through Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1221-1235, July.
    5. Du, Mingyue & Li, Huiqiong & Sun, Jianguo, 2021. "Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    6. S. Eftekhari Mahabadi & M. Ganjali, 2012. "An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2327-2348, July.
    7. Huang, Bin & Wang, Qihua, 2010. "Semiparametric analysis based on weighted estimating equations for transformation models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2078-2090, October.
    8. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    9. Shanshan Li & Yang Ning, 2015. "Estimation of covariate‐specific time‐dependent ROC curves in the presence of missing biomarkers," Biometrics, The International Biometric Society, vol. 71(3), pages 666-676, September.
    10. Menggang Yu & Bin Nan, 2010. "Regression Calibration in Semiparametric Accelerated Failure Time Models," Biometrics, The International Biometric Society, vol. 66(2), pages 405-414, June.
    11. Chengcheng Hu & Victor De Gruttola, 2007. "Joint Modeling of Progression of HIV Resistance Mutations Measured with Uncertainty and Failure Time Data," Biometrics, The International Biometric Society, vol. 63(1), pages 60-68, March.
    12. Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2015. "Double Bias: Estimation of Causal Effects from Length-Biased Samples in the Presence of Confounding," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 69-89, May.
    13. Richard J. Cook & Jerald F. Lawless & Bingfeng Xie, 2022. "Marker-dependent observation and carry-forward of internal covariates in Cox regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 560-584, October.
    14. Ching‐Yun Wang & Xiao Song, 2021. "Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard," Biometrics, The International Biometric Society, vol. 77(2), pages 561-572, June.
    15. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2007. "Simpson’s Paradox for the Cox Model," Discussion Paper Series dp441, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Amélie Detais & Jean-François Dupuy, 2011. "Maximum likelihood estimation in a partially observed stratified regression model with censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1183-1206, December.
    17. Chi-Chung Wen & Chien-Tai Lin, 2011. "Analysis of Current Status Data with Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 760-769, September.
    18. Qiu, Zhiping & Chen, Xiaoping & Zhou, Yong, 2015. "A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 89-97.
    19. Xiaolin Chen & Qihua Wang, 2013. "Semiparametric proportional mean residual life model with covariates missing at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 647-663, September.
    20. Xiaolin Chen & Jianwen Cai, 2018. "Reweighted estimators for additive hazard model with censoring indicators missing at random," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 224-249, April.

    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:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00716-4. 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.