Comparison of Three Parametric Models for Glaucomatous Visual Field Progression Rate Distributions

Area of Science:

• Ophthalmology
• Biostatistics
• Data Science

Background:

• Glaucoma is a progressive optic neuropathy.
• Accurate estimation of visual field progression is crucial for glaucoma management.
• Published data show variability in visual field progression rates.

Purpose of the Study:

• To compare parametric models for fitting visual field progression rate distributions in glaucoma.
• To identify the best-performing statistical model for analyzing glaucoma progression data.

Main Methods:

• Fitted modified Gaussian, Cauchy, and hyperbolic secant models to published visual field progression data from Canada, Sweden, and the US.
• Modified models to independently vary distribution shape on either side of the mode, accommodating asymmetric tails.
• Summed likelihoods across datasets to determine overall model performance.

Main Results:

• The modified hyperbolic secant model was strongly favored over the modified Cauchy model (26.7 log units).
• The modified hyperbolic secant model demonstrated consistent parameter estimates across datasets.
• Parameter variances were low, supporting the utility of Bayesian methods for individual progression estimates.

Conclusions:

• A modified hyperbolic secant model generally performed well for glaucoma visual field progression rate distributions.
• While dataset-specific optimum models varied, the modified hyperbolic secant showed strong overall favorability.
• Averaging distributions, even with inter-study differences, can enhance Bayesian methods for individual glaucoma progression estimation.