A Bayesian Hierarchical Longitudinal Model for Estimation of Central Visual Field Rates of Change in Glaucoma

Individual visual field (VF) sensitivities become unreliable at threshold sensitivities of 19 dB or less, limiting glaucoma monitoring. We evaluated longitudinal variability of central 10° VF measurements based on baseline sensitivity using a Bayesian hierarchical model.

We included 124 glaucoma patients (124 eyes) with central or moderate-to-advanced VF damage, more than 2 years follow-up, and more than 4 central 10-2 VF tests. A Bayesian linear model estimated pointwise change rates, compared with simple linear regression (SLR). Simulations modeled average (-0.21 dB/year) and benchmark (-0.5 dB/year) slopes with residual standard deviations (SD) of 2, 4, 7, or 10 dB. Outcomes included pointwise residual SDs and proportions of significant slopes in cohort and simulations.

The average baseline 10-2 VF mean deviation, follow-up time, and median VF tests were 8.4 ± 5.4 dB, 4.6 ± 0.8 years, and 9 VF tests (range, 4-12 VF tests), respectively. The mean global slopes for Bayesian and SLR models were -0.21 and -0.36 dB/year. Residual SDs were markedly higher when baseline threshold sensitivities was 5 to 20 dB compared with 25 dB or greater. The Bayesian model identified more significant negative slopes, particularly at points with residual SD of less than 4 dB, relative to SLR.

When baseline pointwise sensitivity is 5 to 20 dB, residual variability is very large, substantially reducing the ability to detect glaucoma progression.

Visual field locations with sensitivity near or less than 20 dB demonstrate markedly greater variability over time; thus, excluding these points from visual field algorithms or analytical models could improve efficiency in detecting perimetric progression.