IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v90y2022is1ps37-s51.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12532
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12532?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Molenberghs, Geert & Verbeke, Geert & Iddi, Samuel, 2011. "Pseudo-likelihood methodology for partitioned large and complex samples," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 892-901, July.
    2. Jeonghye Choi & David R. Bell & Leonard M. Lodish, 2012. "Traditional and IS-Enabled Customer Acquisition on the Internet," Management Science, INFORMS, vol. 58(4), pages 754-769, April.
    3. Alexander Robitzsch, 2024. "A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items," Stats, MDPI, vol. 7(3), pages 1-16, June.
    4. Anna Ivanova & Geert Molenberghs & Geert Verbeke, 2017. "Mechanism for missing data incorporated in joint modelling of ordinal responses," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 1049-1064, November.
    5. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    6. Delporte, Margaux & Verbeke, Geert & Fieuws, Steffen & Molenberghs, Geert, 2025. "Accelerating computation: A pairwise fitting technique for multivariate probit models," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    7. Celine Marielle Laffont & Marc Vandemeulebroecke & Didier Concordet, 2014. "Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 955-966, September.
    8. Chuan Hong & Yang Ning & Peng Wei & Ying Cao & Yong Chen, 2017. "A semiparametric model for vQTL mapping," Biometrics, The International Biometric Society, vol. 73(2), pages 571-581, June.
    9. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.
    10. Chiara Brombin & Luigi Salmaso & Lara Fontanella & Luigi Ippoliti, 2015. "Nonparametric combination-based tests in dynamic shape analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 460-484, December.
    11. Casimir Ledoux Sofeu & Virginie Rondeau, 2020. "How to use frailtypack for validating failure-time surrogate endpoints using individual patient data from meta-analyses of randomized controlled trials," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-25, January.
    12. Renfro, Lindsay A. & Shi, Qian & Xue, Yuan & Li, Junlong & Shang, Hongwei & Sargent, Daniel J., 2014. "Center-within-trial versus trial-level evaluation of surrogate endpoints," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 1-20.
    13. Yungtai Lo, 2017. "Joint modeling of bottle use, daily milk intake from bottles, and daily energy intake in toddlers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2301-2316, October.
    14. Myrsini Katsikatsou & Irini Moustaki, 2016. "Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1046-1068, December.
    15. Taban Baghfalaki & Mojtaba Ganjali, 2020. "A transition model for analyzing multivariate longitudinal data using Gaussian copula approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 169-223, June.
    16. Benjamin E. Leiby & Mary D. Sammel & Thomas R. Ten Have & Kevin G. Lynch, 2009. "Identification of multivariate responders and non‐responders by using Bayesian growth curve latent class models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 505-524, September.
    17. Ana Maria Ortega‐Villa & Katherine L. Grantz & Paul S. Albert, 2018. "Estimating onset time from longitudinal and cross‐sectional data with an application to estimating gestational age from longitudinal maternal anthropometry during pregnancy and neonatal anthropometry ," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(3), pages 825-842, June.
    18. T. Baghfalaki & M. Ganjali & D. Berridge, 2014. "Joint modeling of multivariate longitudinal mixed measurements and time to event data using a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1934-1955, September.
    19. Toshihiro Misumi, 2022. "Joint modeling for longitudinal covariate and binary outcome via h-likelihood," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1225-1243, December.
    20. N. Withanage & A.R. de Leon & C.J. Rudnisky, 2014. "Joint estimation of disease-specific sensitivities and specificities in reader-based multi-disease diagnostic studies of paired organs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2282-2297, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:istatr:v:90:y:2022:i:s1:p:s37-s51. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.