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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
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    Cited by:

    1. Wan-Lun Wang & Yu-Chen Yang & Tsung-I Lin, 2024. "Extending finite mixtures of nonlinear mixed-effects models with covariate-dependent mixing weights," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 271-307, June.
    2. 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).
    3. 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.

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