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A joint normal‐binary (probit) model

Author

Listed:
  • Margaux Delporte
  • Steffen Fieuws
  • Geert Molenberghs
  • Geert Verbeke
  • Simeon Situma Wanyama
  • Elpis Hatziagorou
  • Christiane De Boeck

Abstract

In biomedical research, often hierarchical binary and continuous responses need to be jointly modelled. In joint generalised linear mixed models, this can be done with correlated random effects, which allows examining the association structure between the various responses and the evolution of this association over time. In addition, the effect of covariates on all outcomes can be assessed simultaneously. Still, investigating this association is often limited to examining the correlations between the responses on an underlying scale. In addition, the interpretation of this hierarchical model is conditional on the subject‐specific random effects. This paper extends this approach and shows how manifest correlations can be computed, that is, the associations between the observed responses. Further, a marginal model is formulated, in which the interpretation is no longer conditional on the random effects. In addition, prediction intervals are derived of one subvector of responses conditional on the other. These methods are applied in a case study of the lung function and allergic bronchopulmonary aspergillosis in patients with cystic fibrosis.

Suggested Citation

  • Margaux Delporte & Steffen Fieuws & Geert Molenberghs & Geert Verbeke & Simeon Situma Wanyama & Elpis Hatziagorou & Christiane De Boeck, 2022. "A joint normal‐binary (probit) model," International Statistical Review, International Statistical Institute, vol. 90(S1), pages 37-51, December.
    • Handle: RePEc:bla:istatr:v:90:y:2022:i:s1:p:s37-s51
    DOI: 10.1111/insr.12532
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    References listed on IDEAS

    as
    1. Steffen Fieuws & Geert Verbeke, 2006. "Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles," Biometrics, The International Biometric Society, vol. 62(2), pages 424-431, June.
    2. Steffen Fieuws & Geert Verbeke & Filip Boen & Christophe Delecluse, 2006. "High dimensional multivariate mixed models for binary questionnaire data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 449-460, August.
    3. Christopher H. Morrell & Larry J. Brant & Shan Sheng & E. Jeffrey Metter, 2012. "Screening for prostate cancer using multivariate mixed-effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1151-1175, November.
    4. Ariel Alonso & Geert Molenberghs, 2007. "Surrogate Marker Evaluation from an Information Theory Perspective," Biometrics, The International Biometric Society, vol. 63(1), pages 180-186, March.
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