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A Shared Spatial Model for Multivariate Extreme-Valued Binary Data with Non-Random Missingness

Author

Listed:
  • Xiaoyue Zhao

    (Amgen Inc.)

  • Lin Zhang

    (University of Minnesota – Twin Cities)

  • Dipankar Bandyopadhyay

    (Virginia Commonwealth University)

Abstract

Clinical studies and trials on periodontal disease (PD) generate a large volume of data collected at various tooth locations of a subject. However, they present a number of statistical complexities. When our focus is on understanding the extent of extreme PD progression, standard analysis under a generalized linear mixed model framework with a symmetric (logit) link may be inappropriate, as the binary split (extreme disease versus not) maybe highly skewed. In addition, PD progression is often hypothesized to be spatially-referenced, i.e. proximal teeth may have a similar PD status than those that are distally located. Furthermore, a non-ignorable quantity of missing data is observed, and the missingness is non-random, as it informs the periodontal health status of the subject. In this paper, we address all the above concerns through a shared (spatial) latent factor model, where the latent factor jointly models the extreme binary responses via a generalized extreme value regression, and the non-randomly missing teeth via a probit regression. Our approach is Bayesian, and the inferential framework is powered by within-Gibbs Hamiltonian Monte Carlo techniques. Through simulation studies and application to a real dataset on PD, we demonstrate the potential advantages of our model in terms of model fit, and obtaining precise parameter estimates over alternatives that do not consider the aforementioned complexities.

Suggested Citation

  • Xiaoyue Zhao & Lin Zhang & Dipankar Bandyopadhyay, 2021. "A Shared Spatial Model for Multivariate Extreme-Valued Binary Data with Non-Random Missingness," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 374-396, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00198-7
    DOI: 10.1007/s13571-019-00198-7
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    References listed on IDEAS

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    1. Sungduk Kim & Ming-Hui Chen & Dipak K. Dey, 2008. "Flexible generalized t-link models for binary response data," Biometrika, Biometrika Trust, vol. 95(1), pages 93-106.
    2. Roula Tsonaka & Geert Verbeke & Emmanuel Lesaffre, 2009. "A Semi-Parametric Shared Parameter Model to Handle Nonmonotone Nonignorable Missingness," Biometrics, The International Biometric Society, vol. 65(1), pages 81-87, March.
    3. 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.
    4. Dan Li & Xia Wang & Lizhen Lin & Dipak K. Dey, 2016. "Flexible link functions in nonparametric binary regression with Gaussian process priors," Biometrics, The International Biometric Society, vol. 72(3), pages 707-719, September.
    5. Goh, Gyuhyeong & Dey, Dipak K., 2014. "Bayesian model diagnostics using functional Bregman divergence," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 371-383.
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    1. Zhongwei Zhang & Reinaldo B. Arellano‐Valle & Marc G. Genton & Raphaël Huser, 2023. "Tractable Bayes of skew‐elliptical link models for correlated binary data," Biometrics, The International Biometric Society, vol. 79(3), pages 1788-1800, September.

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