A SPATIALLY VARYING HIERARCHICAL RANDOM EFFECTS MODEL FOR LONGITUDINAL MACULAR STRUCTURAL DATA IN GLAUCOMA PATIENTS

• 成果类型: Article
• 署名作者: Su, Erica; Weiss, Robert E.; Nouri-Mahdavi, Kouros; Holbrook, Andrew J.
• 署名单位: University of California System; University of California Los Angeles; University of California System; University of California Los Angeles; University of California Los Angeles Medical Center; David Geffen School of Medicine at UCLA
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/24-AOAS1944
• 发表日期: 2024
• 页码: 3444-3466
• 关键词: cross-covariance functions; optical coherence tomography; multivariate lattice data; visual-field data; asymptotic equivalence; linear-models; progression; validation; coregionalization; statistics

摘要

We model longitudinal macular thickness measurements to monitor the course of glaucoma and prevent vision loss due to disease progression. The macular thickness varies over a 6 x 6 grid of locations on the retina, with additional variability arising from the imaging process at each visit. Currently, ophthalmologists estimate slopes using repeated simple linear regression for each subject and location. To estimate slopes more precisely, we develop a novel Bayesian hierarchical model for multiple subjects with spatially varying population-level and subject-level coefficients, borrowing information over subjects and measurement locations. We augment the model with visit effects to account for observed spatially correlated visit-specific errors. We model spatially varying: (a) intercepts, (b) slopes, and (c) log-residual standard deviations (SD) with multivariate Gaussian process priors with Mat & eacute;rn cross-covariance functions. Each marginal process assumes an exponential kernel with its own SD and spatial correlation matrix. We develop our models for and apply them to data from the Advanced Glaucoma Progression Study. We show that including visit effects in the model reduces error in predicting future thickness measurements and greatly improves model fit.