IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v105y2021i1d10.1007_s10182-020-00389-y.html
   My bibliography  Save this article

Unified approach for regression models with nonmonotone missing at random data

Author

Listed:
  • Yang Zhao

    (University of Regina)

  • Meng Liu

    (Xiamen Golden Strait Investment Co., LTD)

Abstract

Unified approach (Chen and Chen in J R Stat Soc B 62(3):449–460, 2000) uses a working regression model to extract information from auxiliary variables in two-stage study for computing an efficient estimator of regression parameter. As far as we know, the method is limited to deal with missing complete at random data in a simple monotone missing data pattern. In this research, we extend the unified approach to estimate regression models with nonmonotone missing at random data. We describe an inverse probability weighting estimator condition on estimators from a set of working regression models which contains information from incomplete data and auxiliary variables. The proposed method is flexible and can easily accommodate incomplete data and auxiliary variables. We investigate the finite-sample performance of the proposed estimators using simulation studies and further illustrate the estimation method on a case–control study investigating the risk factors of hip fractures.

Suggested Citation

  • Yang Zhao & Meng Liu, 2021. "Unified approach for regression models with nonmonotone missing at random data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 87-101, March.
    • Handle: RePEc:spr:alstar:v:105:y:2021:i:1:d:10.1007_s10182-020-00389-y
    DOI: 10.1007/s10182-020-00389-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-020-00389-y
    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/s10182-020-00389-y?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. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    2. Scheuren, Fritz, 2005. "Multiple Imputation: How It Began and Continues," The American Statistician, American Statistical Association, vol. 59, pages 315-319, November.
    3. Hua Yun Chen & Hui Xie & Yi Qian, 2011. "Multiple Imputation for Missing Values through Conditional Semiparametric Odds Ratio Models," Biometrics, The International Biometric Society, vol. 67(3), pages 799-809, September.
    4. Chatterjee N. & Chen Y-H. & Breslow N.E., 2003. "A Pseudoscore Estimator for Regression Problems With Two-Phase Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 158-168, January.
    5. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    6. Yi‐Hau Chen & Hung Chen, 2000. "A unified approach to regression analysis under double‐sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 449-460.
    7. Hua Yun Chen, 2004. "Nonparametric and Semiparametric Models for Missing Covariates in Parametric Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1176-1189, December.
    8. Chatterjee, Nilanjan & Li, Yan, 2010. "Inference in Semiparametric Regression Models Under Partial Questionnaire Design and Nonmonotone Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 787-797.
    9. J. F. Lawless & J. D. Kalbfleisch & C. J. Wild, 1999. "Semiparametric methods for response‐selective and missing data problems in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 413-438, April.
    10. BaoLuo Sun & Eric J. Tchetgen Tchetgen, 2018. "On Inverse Probability Weighting for Nonmonotone Missing at Random Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 369-379, January.
    11. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    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. Yang Zhao, 2022. "Diagnostic checking of multiple imputation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 271-286, 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. Yang Zhao, 2021. "Semiparametric model for regression analysis with nonmonotone missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 461-475, June.
    2. Zhiwei Zhang & Howard Rockette, 2006. "Semiparametric Maximum Likelihood for Missing Covariates in Parametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 687-706, December.
    3. 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.
    4. Zhuoer Sun & Suojin Wang, 2019. "Semiparametric estimation in regression with missing covariates using single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1201-1232, October.
    5. Yang Zhao, 2022. "Diagnostic checking of multiple imputation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 271-286, June.
    6. Hua Yun Chen & Hui Xie & Yi Qian, 2011. "Multiple Imputation for Missing Values through Conditional Semiparametric Odds Ratio Models," Biometrics, The International Biometric Society, vol. 67(3), pages 799-809, September.
    7. Yang Zhao, 2023. "Maximum likelihood estimation of missing data probability for nonmonotone missing at random data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 197-209, March.
    8. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    9. Breunig, Christoph, 2015. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2015-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. Jonathan S. Schildcrout & Shawn P. Garbett & Patrick J. Heagerty, 2013. "Outcome Vector Dependent Sampling with Longitudinal Continuous Response Data: Stratified Sampling Based on Summary Statistics," Biometrics, The International Biometric Society, vol. 69(2), pages 405-416, June.
    11. Yi Qian & Hui Xie, 2011. "No Customer Left Behind: A Distribution-Free Bayesian Approach to Accounting for Missing Xs in Marketing Models," Marketing Science, INFORMS, vol. 30(4), pages 717-736, July.
    12. Brady Ryan & Ananthika Nirmalkanna & Candemir Cigsar & Yildiz E. Yilmaz, 2023. "Evaluation of Designs and Estimation Methods Under Response-Dependent Two-Phase Sampling for Genetic Association Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 510-539, July.
    13. Haibo Zhou & Rui Song & Yuanshan Wu & Jing Qin, 2011. "Statistical Inference for a Two-Stage Outcome-Dependent Sampling Design with a Continuous Outcome," Biometrics, The International Biometric Society, vol. 67(1), pages 194-202, March.
    14. Samiran Sinha & Krishna K. Saha & Suojin Wang, 2014. "Semiparametric approach for non-monotone missing covariates in a parametric regression model," Biometrics, The International Biometric Society, vol. 70(2), pages 299-311, June.
    15. Breunig, Christoph, 2017. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2017-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    17. Fatema Shafie Khorassani & Jeremy M. G. Taylor & Niko Kaciroti & Michael R. Elliott, 2023. "Incorporating Covariates into Measures of Surrogate Paradox Risk," Stats, MDPI, vol. 6(1), pages 1-23, February.
    18. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    19. Jieli Ding & Tsui-Shan Lu & Jianwen Cai & Haibo Zhou, 2017. "Recent progresses in outcome-dependent sampling with failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 57-82, January.
    20. Jason P. Estes & Bhramar Mukherjee & Jeremy M. G. Taylor, 2018. "Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 568-586, December.

    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:alstar:v:105:y:2021:i:1:d:10.1007_s10182-020-00389-y. 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.