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Finite Mixture of Censored Linear Mixed Models for Irregularly Observed Longitudinal Data

Author

Listed:
  • Francisco H. C. Alencar

    (Universidade Estadual de Campinas)

  • Larissa A Matos

    (Universidade Estadual de Campinas)

  • Víctor H. Lachos

    (University of Connecticut)

Abstract

Linear mixed-effects models are commonly used when multiple correlated measurements are made for each unit of interest. Some inherent features of these data can make the analysis challenging, such as when the series of responses are repeatedly collected for each subject at irregular intervals over time or when the data are subject to some upper and/or lower detection limits of the experimental equipment. Moreover, if units are suspected of forming distinct clusters over time, i.e., heterogeneity, then the class of finite mixtures of linear mixed-effects models is required. This paper considers the problem of clustering heterogeneous longitudinal data in a mixture framework and proposes a finite mixture of multivariate normal linear mixed-effects model. This model allows us to accommodate more complex features of longitudinal data, such as measurement at irregular intervals over time and censored data. Furthermore, we consider a damped exponential correlation structure for the random error to deal with serial correlation among the within-subject errors. An efficient expectation-maximization algorithm is employed to compute the maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the multivariate truncated normal distributions. Furthermore, a general information-based method to approximate the asymptotic covariance matrix is also presented. Results obtained from the analysis of both simulated and real HIV/AIDS datasets are reported to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:3:d:10.1007_s00357-022-09415-x
    DOI: 10.1007/s00357-022-09415-x
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    References listed on IDEAS

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    1. Wan-Lun Wang & Tsung-I Lin, 2015. "Robust model-based clustering via mixtures of skew-t distributions with missing information," 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. 9(4), pages 423-445, December.
    2. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    3. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
    4. 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.
    5. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    6. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    7. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    8. James P. Hughes, 1999. "Mixed Effects Models with Censored Data with Application to HIV RNA Levels," Biometrics, The International Biometric Society, vol. 55(2), pages 625-629, June.
    9. 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.
    10. 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.
    11. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    12. James G. Booth & George Casella & James P. Hobert, 2008. "Clustering using objective functions and stochastic search," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 119-139, February.
    13. Lin, Tsung-I, 2014. "Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 183-195.
    Full references (including those not matched with items on IDEAS)

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