Multivariable Logistic Regression Model: A Novel Mathematical Model that Predicts Visual Field Sensitivity from Macular Ganglion Cell Complex Thickness in Glaucoma

Purpose

To design a mathematical model that can predict the relationship between the ganglion cell complex (GCC) thickness and visual field sensitivity (VFS) in glaucoma patients.

Design

Retrospective cross-sectional case series.

Method

Within 3 months from VFS measurements by the Humphrey field analyzer 10-2 program, 83 eyes underwent macular GCC thickness measurements by spectral-domain optical coherence tomography (SD-OCT). Data were used to construct a multiple logistic model that depicted the relationship between the explanatory variables (GCC thickness, age, sex, and spherical equivalent of refractive errors) determined by a regression analysis and the mean VFS corresponding to the SD-OCT scanned area. Analyses were performed in half or 8 segmented local areas as well as in whole scanned areas. A simple logistic model that included GCC thickness as the single explanatory variable was also constructed. The ability of the logistic models to depict the real GCC thickness/VFS in SAP distribution was analyzed by the χ² test of goodness-of-fit. The significance of the model effect was analyzed by analysis of variance (ANOVA).

Results

Scatter plots between the GCC thickness and the mean VFS showed sigmoid curves. The χ² test of goodness-of-fit revealed that the multiple logistic models showed a good fit for the real GCC thickness/VFS distribution in all areas except the nasal-inferior-outer area. ANOVA revealed that all of the multiple logistic models significantly predicted the VFS based on the explanatory variables. Although simple logistic models also exhibited significant VFS predictability based on the GCC thickness, the model effect was less than that observed for the multiple logistic models.

Conclusions

The currently proposed logistic models are useful methods for depicting relationships between the explanatory variables, including the GCC thickness, and the mean VFS in glaucoma patients.