IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v28y2019i3d10.1007_s11749-018-0603-5.html
   My bibliography  Save this article

Heavy-tailed longitudinal regression models for censored data: a robust parametric approach

Author

Listed:
  • Larissa A. Matos

    (Universidade Estadual de Campinas)

  • Víctor H. Lachos

    (University of Connecticut)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

  • Luis M. Castro

    (Pontificia Universidad Católica de Chile)

Abstract

Longitudinal HIV-1 RNA viral load measures are often subject to censoring due to upper and lower detection limits depending on the quantification assays. A complication arises when these continuous measures present a heavy-tailed behavior because inference can be seriously affected by the misspecification of their parametric distribution. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal distributions. By taking into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure os to allow estimating the parameters of interest and evaluating the log-likelihood function easily and quickly. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained as a byproduct. The practical utility of the proposed method is exemplified using both simulated and real data.

Suggested Citation

  • Larissa A. Matos & Víctor H. Lachos & Tsung-I Lin & Luis M. Castro, 2019. "Heavy-tailed longitudinal regression models for censored data: a robust parametric approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 844-878, September.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0603-5
    DOI: 10.1007/s11749-018-0603-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-018-0603-5
    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/s11749-018-0603-5?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. A. M. Gross, 1973. "A Monte Carlo Swindle for Estimators of Location," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 347-353, November.
    2. 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.
    3. Samson, Adeline & Lavielle, Marc & Mentre, France, 2006. "Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1562-1574, December.
    4. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.
    5. Reinaldo Arellano-Valle & Luis Castro & Graciela González-Farías & Karla Muñoz-Gajardo, 2012. "Student-t censored regression model: properties and inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 453-473, November.
    6. Larissa A. Matos & Luis M. Castro & Víctor H. Lachos, 2016. "Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 627-653, December.
    7. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
    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. Valeriano, Katherine A.L. & Galarza, Christian E. & Matos, Larissa A. & Lachos, Victor H., 2023. "Likelihood-based inference for the multivariate skew-t regression with censored or missing responses," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Graciliano M. S. Louredo & Camila B. Zeller & Clécio S. Ferreira, 2022. "Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 204-242, May.

    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. Larissa A. Matos & Luis M. Castro & Víctor H. Lachos, 2016. "Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 627-653, December.
    2. Marc Lavielle & Adeline Samson & Ana Karina Fermin & France Mentré, 2011. "Maximum Likelihood Estimation of Long-Term HIV Dynamic Models and Antiviral Response," Biometrics, The International Biometric Society, vol. 67(1), pages 250-259, March.
    3. Francisco H. C. Alencar & Larissa A Matos & Víctor H. Lachos, 2022. "Finite Mixture of Censored Linear Mixed Models for Irregularly Observed Longitudinal Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 463-486, November.
    4. Allassonnière, Stéphanie & Chevallier, Juliette, 2021. "A new class of stochastic EM algorithms. Escaping local maxima and handling intractable sampling," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    5. Matos, Larissa A. & Lachos, Victor H. & Balakrishnan, N. & Labra, Filidor V., 2013. "Influence diagnostics in linear and nonlinear mixed-effects models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 450-464.
    6. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    7. 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.
    8. Aldo M. Garay & Victor H. Lachos & Heleno Bolfarine & Celso R. B. Cabral, 2017. "Linear censored regression models with scale mixtures of normal distributions," Statistical Papers, Springer, vol. 58(1), pages 247-278, March.
    9. Gustavo Rocha & Reinaldo Arellano-Valle & Rosangela Loschi, 2015. "Maximum likelihood methods in a robust censored errors-in-variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 857-877, December.
    10. Ibirénoyé Romaric Sodjahin & Fabienne Femenia & Obafemi Philippe Koutchade & A. Carpentier, 2022. "On the economic value of the agronomic effects of crop diversification for farmers: estimation based on farm cost accounting data [Valeur économique des effets agronomiques de la diversification de," Working Papers hal-03639951, HAL.
    11. Wang, Xiaoning & Schumitzky, Alan & D'Argenio, David Z., 2007. "Nonlinear random effects mixture models: Maximum likelihood estimation via the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6614-6623, August.
    12. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    13. Artémis Llamosi & Andres M Gonzalez-Vargas & Cristian Versari & Eugenio Cinquemani & Giancarlo Ferrari-Trecate & Pascal Hersen & Gregory Batt, 2016. "What Population Reveals about Individual Cell Identity: Single-Cell Parameter Estimation of Models of Gene Expression in Yeast," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-18, February.
    14. Baey, Charlotte & Didier, Anne & Lemaire, Sébastien & Maupas, Fabienne & Cournède, Paul-Henry, 2013. "Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model," Ecological Modelling, Elsevier, vol. 263(C), pages 56-63.
    15. Víctor H. Lachos & Celso R. B. Cabral & Marcos O. Prates & Dipak K. Dey, 2019. "Flexible regression modeling for censored data based on mixtures of student-t distributions," Computational Statistics, Springer, vol. 34(1), pages 123-152, March.
    16. A. S. Hedayat & Guoqin Su, 2012. "Robustness of the Simultaneous Estimators of Location and Scale From Approximating a Histogram by a Normal Density Curve," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 25-33, February.
    17. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    18. Allassonnière, Stéphanie & Kuhn, Estelle, 2015. "Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 4-19.
    19. Sodjahin, Romaric & Carpentier, Alain & Koutchade, Obafèmi Philippe & Femenia, Fabienne, 2022. "On the economic value of the agronomic effects of crop diversification for farmers: Estimation based on farm cost accounting data," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322295, Agricultural and Applied Economics Association.
    20. Laura Azzimonti & Francesca Ieva & Anna Maria Paganoni, 2013. "Nonlinear nonparametric mixed-effects models for unsupervised classification," Computational Statistics, Springer, vol. 28(4), pages 1549-1570, 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:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0603-5. 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.