Detection of Fast Progressors: A Bayesian Hierarchical Spatial Model vs. Linear Regression for Detection of Macular Structural Change in Glaucoma

Abstract

Purpose : Test the hypothesis that a novel Bayesian hierarchical spatial longitudinal (HSL) model identifies macular superpixels with rapidly progressing ganglion cell complex (GCC) thickness more efficiently than simple linear regression (SLR).

Methods : We analyzed GCC thickness measurements within 49 macular superpixels in 111 eyes (111 patients) with ≥4 macular optical coherence tomography scans and ≥2 years of follow-up. We estimated superpixel-patient specific slopes and their posterior variances from the latest version of a Bayesian HSL model and Bayesian SLR. A simulation group with known superpixel slopes and variances was created. Outcomes of interest were a) proportion of superpixels with significantly progressing and improving slopes as a function of true slopes in the simulation study and the SLR slope in the cohort in the fastest changing deciles; b) root mean square error (RMSE), and SLR/HSL RMSE ratio within the simulation study and patient cohort. Slopes were defined as significantly negative (positive) if the upper (lower) limit of 95% credible interval was <0 (>0).

Results : Simulation study- Median SLR/HSL RMSE ratio was 1.36 and 1.61 in the top two superpixel deciles with fastest negative rates and 1.73 and 1.31 in the lowest two deciles (most positive slopes); a ratio >1 indicates HSL is better. 83% of RMSE ratios favored HSL in the fastest slope decile. HSL identified a higher proportion of significant negative slopes in the two deciles with the most negative slopes (88% and 57% vs. 52% and 19% for SLR) and 1.9% and 15% of superpixels with the most positive slopes compared to 2.3% and 1.3% for SLR.
Cohort data- The proportion of significantly negative slopes was 77% for SLR and 79% for HSL in the steepest SLR decile. In the most positive SLR decile, HSL and SLR identified 11% and 36% significantly positive slopes. In the fastest 10% of slopes per SLR, SLR/HSL ratio of posterior SDs had a median of 1.83, and 90% of ratios favored HSL. In the most positive 10% of slopes per SLR, this ratio had a median of 2.21, and 94% of SD ratios favored HSL.

Conclusions : A novel Bayesian HSL model improves estimation accuracy of local GCC rates of change regardless of the underlying true rate of change. HSL residual variances are less variable and less likely to capriciously under- or over-estimate significance.

This abstract was presented at the 2023 ARVO Annual Meeting, held in New Orleans, LA, April 23-27, 2023.