A Joint Bayesian Longitudinal Model for Macular Structure–Function Correlations in Glaucoma

Erica Su, PhD; Kwanghyun Lee, MD, PhD; Abraham Liu, MS; Vahid Mohammadzadeh, MD; Sajad Besharati, MD; Joseph Caprioli, MD; Robert E. Weiss, PhD; Kouros Nouri-Mahdavi, MD, MS

doi:10.1016/j.xops.2025.100897

Ophthalmology Science (Nov 2025)

A Joint Bayesian Longitudinal Model for Macular Structure–Function Correlations in Glaucoma

Erica Su, PhD,
Kwanghyun Lee, MD, PhD,
Abraham Liu, MS,
Vahid Mohammadzadeh, MD,
Sajad Besharati, MD,
Joseph Caprioli, MD,
Robert E. Weiss, PhD,
Kouros Nouri-Mahdavi, MD, MS

Affiliations

Erica Su, PhD: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California
Kwanghyun Lee, MD, PhD: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California; Department of Ophthalmology, National Health Insurance Service Ilsan Hospital, Goyang, South Korea
Abraham Liu, MS: Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California
Vahid Mohammadzadeh, MD: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California
Sajad Besharati, MD: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California
Joseph Caprioli, MD: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California
Robert E. Weiss, PhD: Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California
Kouros Nouri-Mahdavi, MD, MS: Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California; Correspondence: Kouros Nouri-Mahdavi, MD, MS, Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, 100Stein Plaza, Los Angeles, CA 90095.

DOI: https://doi.org/10.1016/j.xops.2025.100897
Journal volume & issue: Vol. 5, no. 6
p. 100897

Abstract

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Purpose: To investigate global longitudinal structure–function (SF) relationships between macular ganglion cell complex (GCC) thickness and central visual field (VF) mean deviation (MD) rates of change using a Bayesian joint bivariate longitudinal model. Design: Prospective cohort study. Participants: One hundred seventeen eyes from 117 patients with glaucoma with central damage or moderate to advanced glaucoma were included. Eligible patients had at least 4 visits over a follow-up period of 2 years or longer. Methods: Longitudinal GCC thickness was assessed using optical coherence tomography, and central VF MD was measured with 10-2 standard automated perimetry. A Bayesian joint bivariate longitudinal model was used to estimate random intercepts, slopes, and residual standard deviations (SDs) for structural and functional measures and their correlations. A simulation study compared the Bayesian model (BM)'s performance against simple linear regression (SLR) in estimating these correlations. Main Outcome Measures: Correlations between GCC and MD intercepts, slopes, and residual errors. Results: The mean baseline MD was −8.3 (SD: 5.2) decibels, with an average follow-up period of 5.0 (SD: 0.9) years. The mean correlation was 0.47 (95% credible interval: 0.32 to 0.61) for GCC-MD intercepts (baseline values), 0.29 (95% credible interval: 0.04 to 0.52) for GCC-MD slopes (rates of change), 0.20 (95% credible interval: −0.06 to 0.44) for GCC-MD log residual SDs, and 0.060 (95% credible interval: −0.013, 0.132) for the observation-level GCC-MD residual correlation. The BM consistently demonstrated a smaller root mean squared error than SLR in estimating GCC-MD slope correlations in all simulated scenarios where GCC-MD residual correlation differed from GCC-MD slope correlation. Conclusions: The Bayesian joint model improved accuracy and reduced uncertainty in estimating SF relationships compared to SLR. Correlations between global SF rates of change were significantly positive, although weaker than random intercept correlations. This model represents a key step towards developing local longitudinal SF models to enhance glaucoma progression monitoring. Financial Disclosure(s): Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Published in Ophthalmology Science

ISSN: 2666-9145 (Online)
Publisher: Elsevier
Country of publisher: United States
LCC subjects: Medicine: Ophthalmology
Website: https://www.journals.elsevier.com/ophthalmology-science/

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