Detecting Fast Progressors: Comparing a Bayesian Longitudinal Model to Linear Regression for Detecting Structural Changes in Glaucoma

Abstract

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

Design: Prospective cohort study.

Setting: Tertiary Glaucoma Center.

Subjects: One hundred eleven eyes (111 patients) with moderate to severe glaucoma at baseline and ≥4 macular optical coherence tomography scans and ≥2 years of follow-up.

Observation procedure: Superpixel-patient-specific GCC slopes and their posterior variances in 49 superpixels were derived from our latest Bayesian HSL model and Bayesian SLR. A simulation cohort was created with known intercepts, slopes, and residual variances in individual superpixels.

Main outcome measures: We compared HSL and SLR in the fastest progressing deciles on (1) proportion of superpixels identified as significantly progressing in the simulation study and compared to SLR slopes in cohort data; (2) root mean square error (RMSE), and SLR/HSL RMSE ratios.

Results: Cohort- In the fastest decile of slopes per SLR, 77% and 80% of superpixels progressed significantly according to SLR and HSL, respectively. The SLR/HSL posterior SD ratio had a median of 1.83, with 90% of ratios favoring HSL. Simulation- HSL identified 89% significant negative slopes in the fastest progressing decile vs 64% for SLR. SLR/HSL RMSE ratio was 1.36 for the fastest decile of slopes, with 83% of RMSE ratios favoring HSL.

Conclusion: The Bayesian HSL model improves the estimation efficiency of local GCC rates of change regardless of underlying true rates of change, particularly in fast progressors.