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

Purpose: To compare parametric models for fitting published distributions of visual field progression rates (in dB/yr) for glaucoma. Method: We fitted a modified Gaussian model, a modified Cauchy model and a modified hyperbolic secant model to previously published distributions of visual field progression rates from Canada, Sweden, and the United States. The modification allowed the shape of the model's distribution either side of the mode to be independently varied to allow for the asymmetric tails seen in visual field progression rate distributions. Results: Summing likelihoods across datasets, the modified hyperbolic secant was strongly favored (by 26.7 log units) compared with the next best-fitting model, the modified Cauchy. The modified hyperbolic secant was not the best fit for the Canadian dataset, however. Best-fitting modified hyperbolic secant parameters were broadly similarly between datasets, with parameter variances being less than those expected to negate the benefits of a previously described Bayesian method for improving individual visual field progression rate estimates in glaucoma. Conclusions: Although the optimum model differed depending upon the particular dataset, a modified hyperbolic secant performed well for all distributions investigated and was strongly favored when evidence was summed across datasets. Translational Relevance: Despite differences in the progression rate distributions between studies, the use of an "average" distribution may still be of benefit for improving individual visual field progression rate estimates in glaucoma using Bayesian methods.