Combining structural and functional measurements to improve detection of glaucoma progression using Bayesian hierarchical models

Abstract

Purpose: To present and evaluate a new methodology for combining longitudinal information from structural and functional tests to improve detection of glaucoma progression and estimation of rates of change.

Methods: This observational cohort study included 434 eyes of 257 participants observed for an average of 4.2 ± 1.1 years and recruited from the Diagnostic Innovations in Glaucoma Study (DIGS). The subjects were examined annually with standard automated perimetry, optic disc stereophotographs, and scanning laser polarimetry with enhanced corneal compensation. Rates of change over time were measured using the visual field index (VFI) and average retinal nerve fiber layer thickness (TSNIT average). A bayesian hierarchical model was built to integrate information from the longitudinal measures and classify individual eyes as progressing or not. Estimates of sensitivity and specificity of the bayesian method were compared with those obtained by the conventional approach of ordinary least-squares (OLS) regression.

Results: The bayesian method identified a significantly higher proportion of the 405 glaucomatous and suspect eyes as having progressed when compared with the OLS method (22.7% vs. 12.8%; P < 0.001), while having the same specificity of 100% in 29 healthy eyes. In addition, the bayesian method identified a significantly higher proportion of eyes with progression by optic disc stereophotographs compared with the OLS method (74% vs. 37%; P = 0.001).

Conclusions: A bayesian hierarchical modeling approach for combining functional and structural tests performed significantly better than the OLS method for detection of glaucoma progression. (ClinicalTrials.gov number, NCT00221897.).

Figures

Figure 1.

Proportional Venn diagrams illustrating the number of eyes identified as progressing by the Bayesian and OLS methods, according to the baseline diagnosis. The areas of the circles are proportional to the number of subjects in each category.

Figure 2.

Relationship between slopes of change in the VFI and TSNIT average parameter over time obtained by the Bayesian method. A locally weighted scatterplot smoothing (LOWESS) was fit to the plot.

Figure 3.

ROC curves to discriminate eyes that showed progression on optic disc stereophotographs versus healthy eyes for the Bayesian and OLS methods.

Figure 4.

Relationship between slopes of change in the VFI and TSNIT average parameter over time obtained by the OLS linear regression method. A locally weighted scatterplot smoothing (LOWESS) was fit to the plot.

Figure 5.

Proportional Venn diagrams illustrating the agreement between the Bayesian and OLS methods in detecting structural (TSNIT average) and functional (standard automated perimetry visual field index [VFI]) change over time. The areas of the circles are proportional to the number of subjects in each category.

Figure 6.

(A) SAP and SLP results in an eye that had progressive glaucomatous optic neuropathy over time on optic disc stereophotographs. There was progressive RNFL thinning, as shown by the color-coded map and a decrease in TSNIT average values over time. SAP shows progressive visual field defect on the superior nasal sector. (B) Slopes of change for VFI and TSNIT average obtained by OLS regression and the combined Bayesian method for the examinations shown in (A). The OLS regression slope for VFI was not statistically significant, whereas the Bayesian VFI slope was significantly less than 0. The Bayesian slope for the functional test (VFI) was influenced by the presence of significant changes in the structural test (TSNIT average). The graph shows the kernel density estimate for the posterior distribution of the slope of VFI change obtained by the Bayesian hierarchical model.