IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v33y2018i4d10.1007_s00180-018-0812-0.html
   My bibliography  Save this article

Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies

Author

Listed:
  • Yuzhu Tian

    (Henan University of Science and Technology
    Central University Of Finance and Economics)

  • Manlai Tang

    (Hang Seng Management College)

  • Maozai Tian

    (Renmin University of China)

Abstract

It is very common in AIDS studies that response variable (e.g., HIV viral load) may be subject to censoring due to detection limits while covariates (e.g., CD4 cell count) may be measured with error. Failure to take censoring in response variable and measurement errors in covariates into account may introduce substantial bias in estimation and thus lead to unreliable inference. Moreover, with non-normal and/or heteroskedastic data, traditional mean regression models are not robust to tail reactions. In this case, one may find it attractive to estimate extreme causal relationship of covariates to a dependent variable, which can be suitably studied in quantile regression framework. In this paper, we consider joint inference of mixed-effects quantile regression model with right-censored responses and errors in covariates. The inverse censoring probability weighted method and the orthogonal regression method are combined to reduce the biases of estimation caused by censored data and measurement errors. Under some regularity conditions, the consistence and asymptotic normality of estimators are derived. Finally, some simulation studies are implemented and a HIV/AIDS clinical data set is analyzed to to illustrate the proposed procedure.

Suggested Citation

  • Yuzhu Tian & Manlai Tang & Maozai Tian, 2018. "Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies," Computational Statistics, Springer, vol. 33(4), pages 1563-1587, December.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-018-0812-0
    DOI: 10.1007/s00180-018-0812-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0812-0
    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/s00180-018-0812-0?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. Liu Yuan & Bottai Matteo, 2009. "Mixed-Effects Models for Conditional Quantiles with Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-24, November.
    2. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    3. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    4. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    5. Noh, Maengseok & Wu, Lang & Lee, Youngjo, 2012. "Hierarchical likelihood methods for nonlinear and generalized linear mixed models with missing data and measurement errors in covariates," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 42-51.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Heejung Bang & Anastasios A. Tsiatis, 2002. "Median Regression with Censored Cost Data," Biometrics, The International Biometric Society, vol. 58(3), pages 643-649, September.
    8. Vaida, Florin & Fitzgerald, Anthony P. & DeGruttola, Victor, 2007. "Efficient hybrid EM for linear and nonlinear mixed effects models with censored response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5718-5730, August.
    9. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    10. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    11. Yangxin Huang & Getachew Dagne, 2012. "Bayesian Semiparametric Nonlinear Mixed-Effects Joint Models for Data with Skewness, Missing Responses, and Measurement Errors in Covariates," Biometrics, The International Biometric Society, vol. 68(3), pages 943-953, September.
    12. Antonio F. Galvao & Carlos Lamarche & Luiz Renato Lima, 2013. "Estimation of Censored Quantile Regression for Panel Data With Fixed Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1075-1089, September.
    13. Yangxin Huang & Getachew Dagne, 2011. "A Bayesian Approach to Joint Mixed-Effects Models with a Skew-Normal Distribution and Measurement Errors in Covariates," Biometrics, The International Biometric Society, vol. 67(1), pages 260-269, March.
    14. Wu L., 2002. "A Joint Model for Nonlinear Mixed-Effects Models With Censoring and Covariates Measured With Error, With Application to AIDS Studies," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 955-964, 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. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    2. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    3. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    4. Christian E. Galarza & Luis M. Castro & Francisco Louzada & Victor H. Lachos, 2020. "Quantile regression for nonlinear mixed effects models: a likelihood based perspective," Statistical Papers, Springer, vol. 61(3), pages 1281-1307, June.
    5. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    6. Zongwu Cai & Meng Shi & Yue Zhao & Wuqing Wu, 2020. "Testing Financial Hierarchy Based on A PDQ-CRE Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202011, University of Kansas, Department of Economics, revised Jul 2020.
    7. Hao Cheng & Ying Wei, 2018. "A fast imputation algorithm in quantile regression," Computational Statistics, Springer, vol. 33(4), pages 1589-1603, December.
    8. Chen, Xuerong & Tang, Niansheng & Zhou, Yong, 2016. "Quantile regression of longitudinal data with informative observation times," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 176-188.
    9. Damian Clarke & Manuel Llorca Jaña & Daniel Pailañir, 2023. "The use of quantile methods in economic history," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 56(2), pages 115-132, April.
    10. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    11. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    12. Xiao, Zhijie & Xu, Lan, 2019. "What do mean impacts miss? Distributional effects of corporate diversification," Journal of Econometrics, Elsevier, vol. 213(1), pages 92-120.
    13. Yuanshan Wu & Yanyuan Ma & Guosheng Yin, 2015. "Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1670-1683, December.
    14. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    15. Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    16. Yuzhu Tian & Manlai Tang & Yanchao Zang & Maozai Tian, 2018. "Quantile regression for linear models with autoregressive errors using EM algorithm," Computational Statistics, Springer, vol. 33(4), pages 1605-1625, December.
    17. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    18. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    19. Ali Aghamohammadi, 2018. "Bayesian analysis of dynamic panel data by penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 91-108, March.
    20. Xiaoming Lu & Zhaozhi Fan, 2020. "Generalized linear mixed quantile regression with panel data," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.

    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:33:y:2018:i:4:d:10.1007_s00180-018-0812-0. 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.