Su By Erica, Weiss Robert E, Nouri-Mahdavi Kouros, Holbrook Andrew J
Department of Biostatistics, Fielding School of Public Health, University of California, Los Angeles.
Glaucoma Division, Stein Eye Institute, David Geffen School of Medicine, University of California, Los Angeles.
Ann Appl Stat. 2024 Dec;18(4):3444-3466. doi: 10.1214/24-aoas1944. Epub 2024 Oct 31.
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 × 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 Matérn 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.
我们对黄斑厚度的纵向测量进行建模，以监测青光眼的病程并预防因疾病进展导致的视力丧失。黄斑厚度在视网膜上6×6的位置网格上变化，每次就诊时成像过程还会产生额外的变异性。目前，眼科医生针对每个受试者和位置使用重复简单线性回归来估计斜率。为了更精确地估计斜率，我们为多个受试者开发了一种新颖的贝叶斯分层模型，该模型具有空间变化的总体水平和受试者水平系数，可在受试者和测量位置之间借用信息。我们通过就诊效应来增强模型，以考虑观察到的特定于就诊的空间相关误差。我们对空间变化的（a）截距、（b）斜率和（c）对数残差标准差（SD）进行建模，使用具有马特恩交叉协方差函数的多元高斯过程先验。每个边缘过程都假定具有自己的标准差和空间相关矩阵的指数核。我们开发了这些模型并将其应用于高级青光眼进展研究的数据。我们表明，在模型中纳入就诊效应可减少预测未来厚度测量的误差，并大大改善模型拟合。
