Detecting glaucomatous change in visual fields: Analysis with an optimization framework

Abstract

Detecting glaucomatous progression is an important aspect of glaucoma management. The assessment of longitudinal series of visual fields, measured using Standard Automated Perimetry (SAP), is considered the reference standard for this effort. We seek efficient techniques for determining progression from longitudinal visual fields by formulating the problem as an optimization framework, learned from a population of glaucoma data. The longitudinal data from each patient's eye were used in a convex optimization framework to find a vector that is representative of the progression direction of the sample population, as a whole. Post-hoc analysis of longitudinal visual fields across the derived vector led to optimal progression (change) detection. The proposed method was compared to recently described progression detection methods and to linear regression of instrument-defined global indices, and showed slightly higher sensitivities at the highest specificities than other methods (a clinically desirable result). The proposed approach is simpler, faster, and more efficient for detecting glaucomatous changes, compared to our previously proposed machine learning-based methods, although it provides somewhat less information. This approach has potential application in glaucoma clinics for patient monitoring and in research centers for classification of study participants.

Keywords: Change detection; Computational modeling; Data mining; Glaucoma; Progression; Standard automated perimetry; Visual field.

Figure 1

SAP visual field collection, a sample pattern, and data vector.

Figure 2

Pipeline for progression detection using optimization framework.

Figure 3

Preprocessing: Longitudinal SAP visual fields and feature vector creation.

Figure 4

Glaucoma boundary limit specification. Projecting the visual field data vectors on the objective vector x and estimating the slope using linear regression. P₀ to P₅ indicate six longitudinal visual field data vectors for an eye. S₀ to S₅ indicate the projected values on the objective vector x.

Figure 5

Distribution of the linear regression slopes of the projected visual fields data vectors of all eyes in the stable group on the objective vector x. The blue line indicates the left tail 95^th percentile.

Figure 6

Progression detection by the proposed optimization framework in two sample eyes. The gray line indicates the 95th percentile limit. The orange circles represent the actual projected visual field values on objective vector x, and the blue circles are linear regression approximations of the orange circles. The eye in the left panel is classified as progressed and the eye in the right panel is classified as non-progressed.

Figure 7

Partial ROC curve showing sensitivity versus 1-specificity of CDOF, VIM, GEM, PoPLR, PLR (based on two significant deteriorating locations), PLR (based on three significant deteriorating locations), linear regression of MD and linear regression VFI over time.