Improved Estimation of Rates of Glaucoma Progression Using Spatial Two-Fold Linear Mixed Models

Abstract

Visual field testing is essential for detecting glaucomatous damage. Traditional approaches such as pointwise linear regression often fail to account for the spatial correlations and hierarchical structure among test locations. We propose a two-fold linear mixed model that incorporates both eye-level and within-eye cluster-level random effects. Using the Bascom Palmer Glaucoma Repository, we show that our model outperforms conventional pointwise linear regression and permutation-based pointwise regression. In simulation studies, the proposed method yields markedly lower mean squared error than ordinary least squares, achieving MSEs of 0.41 (lower eye) and 0.50 (upper eye), compared with 1.12 and 1.72, respectively, while also reducing false-positive and false-negative rates. This framework provides improved precision and interpretability for quantifying visual field progression in glaucoma.