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Abstract:
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We model macular thickness measurements over time and location to monitor glaucoma deterioration and prevent vision loss. Data characteristics vary over a 6×6 grid of locations on the retina with additional variability arising from the imaging process at each visit. Currently, physicians estimate slopes using repeated simple linear regression for each subject and location. We develop a novel Bayesian hierarchical model with spatially varying population-level and subject-specific coefficients with visit effects, accounting for both spatial and within-subject correlation, leading to more precision in estimating slopes. We employ correlated spatially varying a) intercepts, b) slopes, and c) residual standard deviations (SD) by treating these parameter fields as multivariate Gaussian processes with flexible Matérn cross-covariance functions. Each marginal process assumes an exponential kernel with its own SD and spatial correlation matrix. We apply our model to data from the Advanced Glaucoma Progression Study, providing insight to the correlations between the spatially varying processes at the population and subject levels.
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