Estimating Ganglion Cell Complex Rates of Change With Bayesian Hierarchical Models

Abstract

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

Multivariate Longitudinal Modeling of Macular Ganglion Cell Complex

“…We omitted all data from visits less than 0.2 years after a previous visit. 13 The study adhered to the tenets of the Declaration of Helsinki, was approved by UCLA's…”

“…12,23 A multivariate hierarchical longitudinal model Our data cleaning methods have been described previously and we provide details in the web appendix. 13 We inspected profile plots and empirical summary plots of outcomes for all subjects and all superpixels. 15 We removed zero values as erroneous, and we identified and removed outliers that caused large increases/decreases between consecutive measurements; details of the outlier removal algorithm are given in the web appendix section titled "Outlier Removal Algorithm for 49 Superpixels".…”

“…2,3,5,10,11 Our research group has shown that ganglion cell complex (GCC), which is the sum of macular RNFL, ganglion cell layer (GCL) and inner plexiform layer (IPL), could be the preferred outcome measure for establishing glaucoma progression in the macular region. 12,13 We recently proposed and implemented a random intercept and random slope Bayesian hierarchical model for estimating population average and individual rates of change at the level of 3°×3° macular superpixels in a cohort of patients with central damage or moderate to advanced glaucoma. Our model also included a subject-specific random variance for superpixel residuals.…”

“…Our model also included a subject-specific random variance for superpixel residuals. [13][14][15][16][17][18][19] In this model, information from the entire cohort is used to efficiently estimate individual intercepts and slopes for each superpixel. Compared to simple linear regression of thickness measurements against time in a single superpixel for a single subject, the hierarchical model more efficiently estimates individual slopes and provides population estimates.…”

“…[14][15][16][17][18] Our initial random intercept and random slope model was fit to all subjects' longitudinal data from a single superpixel and did not attempt to model correlations of population or individual parameters across superpixels. 13 While the cross-sectional correlation of the 10-2 visual field test locations have been previously explored, 20 there is no information in the published literature on cross-sectional or longitudinal correlations among thickness J o u r n a l P r e -p r o o f measurements of superpixels across the macula. Constructing an appropriate longitudinal model for macular thickness that incorporates spatial and temporal relationships holds the possibility of improved estimation of subject-level slopes over the single superpixel hierarchical model and potentially allows us to make accurate global statements about the probability of glaucoma progression across the macula.…”