A Statistical Model to Analyze Clinician Expert Consensus on Glaucoma Progression using Spatially Correlated Visual Field Data

Abstract

Purpose: We developed a statistical model to improve the detection of glaucomatous visual field (VF) progression as defined by the consensus of expert clinicians.

Methods: We developed new methodology in the Bayesian setting to properly model the progression status of a patient (as determined by a group of expert clinicians) as a function of changes in spatially correlated sensitivities at each VF location jointly. We used a spatial probit regression model that jointly incorporates all highly correlated VF changes in a single framework while accounting for structural similarities between neighboring VF regions.

Results: Our method had improved model fit and predictive ability compared to competing models as indicated by the deviance information criterion (198.15 vs. 201.29-213.38), a posterior predictive model selection metric (130.08 vs. 142.08-155.59), area under the receiver operating characteristic curve (0.80 vs. 0.59-0.72; all P values < 0.018), and optimal sensitivity (0.92 vs. 0.28-0.82). Simulation study results suggest that estimation (reduction of mean squared errors) and inference (correct coverage of 95% credible intervals) for the model parameters are improved when spatial modeling is incorporated.

Conclusions: We developed a statistical model for the detection of VF progression defined by clinician expert consensus that accounts for spatially correlated changes in visual sensitivity over time, and showed that it outperformed competing models in a number of areas.

Translational relevance: This model may easily be incorporated into routine clinical practice and be useful for detecting glaucomatous VF progression defined by clinician expert consensus.

Keywords: conditional autoregressive model; glaucoma progression; spatially correlated predictors; spatially varying coefficients; visual field.

Figure 1

Visual field regions (A) mapped to the optic disc (B). The numbers represent the spatial locations associated with the η(s_j) parameters. BS, blind spot.

Figure 2

Posterior means from (A) Model 1, (B) Model 2, and (C) Model 3 for the spatial slopes across the visual field. The posterior standard deviations for the presented parameters ranged from 6.98 to 11.34 with a median value of 8.51 for Model 1, 34.52 to 122.50 with a median value of 56.43 for Model 2, and was 0.75 for Model 3. The Monte Carlo standard errors for the presented estimated posterior means ranged from 0.01 to 0.05 with a median value of 0.02 for Model 1, 0.15 to 1.15 with a median value of 0.39 for Model 2, and was 0.001 for Model 3.

Figure 3

Receiver operating characteristic (ROC) curve plots with AUC curves listed in parentheses. Model 2 is omitted due to overfitting.