A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in Glaucoma Eyes

Abstract

Purpose : Longitudinal analyses of local structural or functional measures frequently use repeated simple linear regression (SLR) to estimate eye-specific rates of change (RoC). We developed a novel Bayesian hierarchical spatial longitudinal (HSL) model to improve estimation of local macular structural RoC in a prospective cohort of glaucoma patients and compared the results to those of SLR.

Methods : 111 eyes (111 patients) from the Advanced Glaucoma Progression Study with 4 OCT scans and 2 years of follow-up were included. Ganglion cell complex (GCC) thickness within 7x7 arrays of superpixels from Spectralis OCT macular volume scans were exported and analyzed. The current version of our Bayesian HSL model includes superpixel intercept and slope random effects, global patient intercept and slope effects, patient-superpixel interaction intercepts and slopes, and visit effects to improve accuracy of superpixel-patient RoC estimates. Superpixel-patient specific estimates and their posterior variances were calculated from the HSL model and compared with those obtained from Bayesian SLR performed on longitudinal data from each superpixel-patient separately. We considered superpixel-patient specific RoC as worsening or improving (significantly negative or positive) when the upper or lower limit of the 95% credible interval was less than or higher than 0, respectively.

Results : Mean (SD) baseline 10-2 visual field mean deviation was –8.9 (5.9) dB. Mean (SD) follow-up time was 3.6 (0.4) years with 7.3 (1.1) OCT scans per eye. Across 5,419 superpixel-patient curves, the posterior variances from HSL were smaller than SLR for 87% of intercepts and 83% of slopes. The mean (IQR) ratio of posterior variances of SLR over HSL for intercepts and slopes were 4.0 (1.5-4.9) and 3.9 (1.3-4.4), respectively. HSL identified a higher proportion of significant negative slopes (17.6% vs. 15.6%; p<.001) and lower proportion of significant positive slopes (1.2% vs. 4.6%; p<.001) as compared to SLR.

Conclusions : A novel Bayesian HSL model improves estimation accuracy of local GCC rates of change. The proposed model is 4 times as efficient as SLR for estimating superpixel-patient intercepts or slopes and identifies a higher proportion of deteriorating superpixels when compared to SLR while minimizing false positive detection rates.

This abstract was presented at the 2022 ARVO Annual Meeting, held in Denver, CO, May 1-4, 2022, and virtually.