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Estimating the Distribution of True Rates of Visual Field Progression in Glaucoma

Montesano, G. ORCID: 0000-0002-9148-2804, Crabb, D. P. ORCID: 0000-0001-8611-1155, Wright, D. M. , Rabiolo, A., Ometto, G. ORCID: 0000-0002-0900-4847 & Garway-Heath, D. F. (2024). Estimating the Distribution of True Rates of Visual Field Progression in Glaucoma. Translational Vision Science & Technology, 13(4), article number 15. doi: 10.1167/tvst.13.4.15


Purpose: The purpose of this study was to estimate the distribution of the true rates of progression (RoP) of visual field (VF) loss. .

Methods: We analyzed the progression of mean deviation over time in series of ≥ 10 tests from 3352 eyes (one per patient) from 5 glaucoma clinics, using a novel Bayesian hierarchical Linear Mixed Model (LMM); this modeled the random-effect distribution of RoPs as the sum of 2 independent processes following, respectively, a negative exponential distribution (the "true" distribution of RoPs) and a Gaussian distribution (the "noise"), resulting in a skewed exGaussian distribution. The exGaussian-LMM was compared to a standard Gaussian-LMM using the Watanabe-Akaike Information Criterion (WAIC). The random-effect distributions were compared to the empirical cumulative distribution function (eCDF) of linear regression RoPs using a Kolmogorov-Smirnov test.

Results: The WAIC indicated a better fit with the exGaussian-LMM (estimate [standard error]: 192174.4 [721.2]) than with the Gaussian-LMM (192595 [697.4], with a difference of 157.2 [22.6]). There was a significant difference between the eCDF and the Gaussian-LMM distribution (P < 0.0001), but not with the exGaussian-LMM distribution (P = 0.108). The estimated mean (95% credible intervals, CIs) "true" RoP (-0.377, 95% CI = -0.396 to -0.359 dB/year) was more negative than the observed mean RoP (-0.283, 95% CI = -0.299 to -0.268 dB/year), indicating a bias likely due to learning in standard LMMs.

Conclusions: The distribution of "true" RoPs can be estimated with an exGaussian-LMM, improving model accuracy.

Translational Relevance: We used these results to develop a fast and accurate analytical approximation for sample-size calculations in clinical trials using standard LMMs, which was integrated in a freely available web application.

Publication Type: Article
Additional Information: This work is licensed under a Creative Commons Attribution 4.0 International License.
Publisher Keywords: visual field (VF); perimetry; glaucoma; progression; hierarchical modeling
Subjects: R Medicine > RE Ophthalmology
Departments: School of Health & Psychological Sciences
School of Health & Psychological Sciences > Optometry & Visual Sciences
SWORD Depositor:
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Available under License Creative Commons: Attribution International Public License 4.0.

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