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Activity Number: 557 - New Directions in Bayesian Methods for Longitudinal and Graph Data
Type: Contributed
Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #323194
Title: A Bayesian Hierarchical Spatially Varying Coefficients Model for Longitudinal Structural Data in Glaucomatous Eyes
Author(s): Erica Su* and Andrew Holbrook and Robert Erin Weiss and Kouros Nouri-Mahdavi
Companies: UCLA Biostatistics and UCLA Biostatistics and UCLA Biostatistics and UCLA Stein Eye Institute
Keywords: Bayesian modeling; Bayesian nonparametrics; multivariate Gaussian processes; random effects; spatially varying coefficients

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.

Authors who are presenting talks have a * after their name.

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