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A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in
Erica Su1, Vahid Mohammadzadeh2, Massood Mohammadi2
1Department of Biostatistics, Fielding School of Public Health, University of California Los Angeles, Los Angeles, California, USA.
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.
