Estimating Ganglion Cell Complex Rates of Change With Bayesian Hierarchical Models

Develop a hierarchical longitudinal regression model for estimating local rates of change of macular ganglion cell complex (GCC) measurements with optical coherence tomography (OCT).

We enrolled 112 eyes with four or more macular OCT images and ≥2 years of follow-up. GCC thickness measurements within central 6 × 6 superpixels were extracted from macular volume scans. We fit data from each superpixel separately with several hierarchical Bayesian random-effects models. Models were compared with the Watanabe-Akaike information criterion. For our preferred model, we estimated population and individual slopes and intercepts (baseline thickness) and their correlation.

Mean (SD) follow-up time and median (interquartile range) baseline 24-2 visual field mean deviation were 3.6 (0.4) years and -6.8 (-12.2 to -4.3) dB, respectively. The random intercepts and slopes model with random residual variance was the preferred model. While more individual and population negative slopes were observed in the paracentral and papillomacular superpixels, superpixels in the superotemporal and inferior regions displayed the highest correlation between baseline thickness and rates of change (r = -0.43 to -0.50 for the top five correlations).

A Bayesian linear hierarchical model with random intercepts/slopes and random variances is an optimal initial model for estimating GCC slopes at population and individual levels. This novel model is an efficient method for estimating macular rates of change and probability of glaucoma progression locally.

The proposed Bayesian hierarchical model can be applied to various macular outcomes from different OCT devices and to superpixels of variable sizes to estimate local rates of change and progression probability.