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

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.