A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in Glaucomatous Eyes.
Su Erica, Mohammadzadeh Vahid, Mohammadi Massood, Shi Lynn, Law Simon K, Coleman Anne L, Caprioli Joseph, Weiss Robert E, Nouri-Mahdavi Kouros
AI Summary
A new statistical model (Bayesian HSL) more accurately tracks macular nerve fiber layer thinning in glaucoma than standard methods, enabling earlier and more efficient detection of disease progression.
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.
MeSH Terms
Shields Classification
Key Concepts6
A novel Bayesian hierarchical spatial longitudinal (HSL) model improved the estimation of local macular ganglion cell complex (GCC) rates of change compared to simple linear regression (SLR) and a conditional autoregressive (CAR) model in an analysis of 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.
The HSL model 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 simple linear regression (SLR) in an analysis of 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.
In a simulation study comparing the accuracy of intercept and slope estimates in individual superpixels, the median (tenth, ninetieth percentile) ratio of mean squared error of simple linear regression (SLR) over the Bayesian HSL model for intercepts and slopes were 1.91 (1.23, 2.75) and 3.25 (1.40, 10.14), respectively.
In a simulation study comparing the accuracy of intercept and slope estimates in individual superpixels, the median (tenth, ninetieth percentile) ratio of mean squared error of a conditional autoregressive (CAR) model over the Bayesian HSL model for intercepts and slopes were 1.51 (1.05, 2.20) and 2.36 (1.17, 5.56), respectively.
The novel Bayesian HSL model is more than twice as efficient as simple linear regression (SLR) for estimating superpixel-patient slopes and identifies a higher proportion of deteriorating superpixels than SLR while minimizing false-positive detection rates.
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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