Measuring Glaucoma Progression Using a Common Factor Model

Abstract

 

Purpose

 

To construct a common factor (CF) model to determine what the visual field [VF] measurements (mean deviation [MD], pattern standard deviation [PSD], and visual field index [VFI]) have in common and what is unique to each. The common factor can then be estimated and used as an optimal index for glaucoma progression.

 

Methods

 

MD, PSD, VFI, baseline age, and glaucoma diagnosis (healthy [H] vs glaucoma [G]) were available for 57 subjects. Ages ranged from 41-76 yrs. 32% (18) of left and 39% (22) of right eyes had glaucoma. CF model is illustrated by the path diagram (Figure). True CF slopes for each eye are represented by latent variables (OS & OD) which were scaled to have mean 0 and standard deviation (SD) 1. VF slopes were also linearly transformed to mean 0 and SD 1 so that the factor loadings (λ1 for MD, λ2 for PSD, and λ3 for VFI) represent the correlation between each VF measurement and the latent CF slope. The residual error variances (e1, e2, an e3) equal 1-.λ². The latent factors OS and OD were allowed to have correlation ρ. Each latent factor was dependent on age and diagnosis (H=0, G=1). Onyx visual SEM software produced the path diagram and initial parameter estimates shown in Figure. Onyx cannot currently include constraints necessary for the residual error variances but was used to generate the equivalent OpenMx SEM code. This code was then modified to include the constraints. R software for statistical computing was used to determine the full information maximum likelihood parameter estimates.

 

Results

 

Parameter estimates and 95% confidence intervals are shown in Table. ρ was 0.508 and was statistically significant (SS). Age effect was near zero and not SS. The effect for diagnosis showed that the latent progression slope for eyes with glaucoma was lower than for healthy and the difference was SS. The correlations between the visual field measurements and the latent progression factors were similar for MD and PSD (ratio not SS) and substantially lower than for VFI (SS). Thus VFI was the most precise at assessing glaucoma progression.

 

Conclusions

 

<br /> The CF model calibrated the VF measurements and determined what they had in common (λ) and what was unique (e). VFI was shown to be substantially more precise than both MD and PSD and the CF slopes differed between healthy and glaucoma.