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Bayesian multivariate nonlinear mixed models for censored longitudinal trajectories with non-monotone missing values

Author

Listed:
  • Wan-Lun Wang

    (National Cheng Kung University)

  • Luis M. Castro

    (Pontificia Universidad Católica de Chile and Center for the Discovery of Structures in Complex Data)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

The analysis of multivariate longitudinal data may often encounter a difficult task, particularly in the presence of censored measurements induced by detection limits and intermittently missing values arising when subjects do not respond to a part of outcomes during scheduled visits. The multivariate nonlinear mixed model (MNLMM) has emerged as a promising analytical tool for multi-outcome longitudinal data following arbitrarily nonlinear profiles with random phenomena. This article presents a generalization of the MNLMM, called MNLMM-CM, designed to simultaneously accommodate the effects of censorship and missingness within a Bayesian framework. Specifically, we develop a Markov chain Monte Carlo procedure that combines a Gibbs sampler with the Metropolis–Hastings algorithm. This hybrid approach facilitates Bayesian estimation of essential model parameters and imputation of non-responses under the missing at random mechanism. The issue of posterior predictive inference for the censored and missing outcomes is also addressed. The effectiveness and performance of the proposed methodology are demonstrated through the analysis of simulated data and a real example from an AIDS clinical study.

Suggested Citation

  • Wan-Lun Wang & Luis M. Castro & Tsung-I Lin, 2024. "Bayesian multivariate nonlinear mixed models for censored longitudinal trajectories with non-monotone missing values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(5), pages 585-605, July.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:5:d:10.1007_s00184-023-00929-x
    DOI: 10.1007/s00184-023-00929-x
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    References listed on IDEAS

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    1. Wolfinger, Russell D. & Xihong Lin, 1997. "Two Taylor-series approximation methods for nonlinear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 465-490, September.
    2. Joseph Ibrahim & Geert Molenberghs, 2009. "Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 1-43, May.
    3. Joseph Ibrahim & Geert Molenberghs, 2009. "Rejoinder on: Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 68-75, May.
    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Shu Xu & Shelley A. Blozis, 2011. "Sensitivity Analysis of Mixed Models for Incomplete Longitudinal Data," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 237-256, April.
    6. Guillermo Marshall & Rolando De la Cruz-Mesía & Fernando A. Quintana & Anna E. Barón, 2009. "Discriminant Analysis for Longitudinal Data with Multiple Continuous Responses and Possibly Missing Data," Biometrics, The International Biometric Society, vol. 65(1), pages 69-80, March.
    7. 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.
    8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    9. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, September.
    10. 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.
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