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Su E, Mohammadzadeh V, Mohammadi M, Shi L, Law SK, Coleman AL, Caprioli J, Weiss RE, Nouri-Mahdavi K. A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in Glaucomatous Eyes. Transl Vis Sci Technol 2024; 13:26. [PMID: 38285459 PMCID: PMC10829804 DOI: 10.1167/tvst.13.1.26] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2022] [Accepted: 12/06/2023] [Indexed: 01/30/2024] Open
Abstract
Purpose Demonstrate that a novel Bayesian hierarchical spatial longitudinal (HSL) model improves estimation of local macular ganglion cell complex (GCC) rates of change compared to simple linear regression (SLR) and a conditional autoregressive (CAR) model. Methods We analyzed GCC thickness measurements within 49 macular superpixels in 111 eyes (111 patients) with four or more macular optical coherence tomography scans and two or more years of follow-up. We compared superpixel-patient-specific estimates and their posterior variances derived from the latest version of a recently developed Bayesian HSL model, CAR, and SLR. We performed a simulation study to compare the accuracy of intercept and slope estimates in individual superpixels. Results HSL identified a significantly higher proportion of significant negative slopes in 13/49 superpixels and a significantly lower proportion of significant positive slopes in 21/49 superpixels than SLR. In the simulation study, the median (tenth, ninetieth percentile) ratio of mean squared error of SLR [CAR] over HSL for intercepts and slopes were 1.91 (1.23, 2.75) [1.51 (1.05, 2.20)] and 3.25 (1.40, 10.14) [2.36 (1.17, 5.56)], respectively. Conclusions A novel Bayesian HSL model improves estimation accuracy of patient-specific local GCC rates of change. The proposed model is more than twice as efficient as SLR for estimating superpixel-patient slopes and identifies a higher proportion of deteriorating superpixels than SLR while minimizing false-positive detection rates. Translational Relevance The proposed HSL model can be used to model macular structural measurements to detect individual glaucoma progression earlier and more efficiently in clinical and research settings.
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Affiliation(s)
- Erica Su
- Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California, USA
| | - Vahid Mohammadzadeh
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Massood Mohammadi
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Lynn Shi
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Simon K Law
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Anne L Coleman
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Joseph Caprioli
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
| | - Robert E Weiss
- Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California, USA
| | - Kouros Nouri-Mahdavi
- Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, USA
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