青光眼患者黄斑纵向结构数据的空间变化分层随机效应模型
A Spatially Varying Hierarchical Random Effects Model for Longitudinal Macular Structural Data in Glaucoma Patients
摘要：
我们对纵向黄斑厚度测量进行建模，以监测青光眼的病程并防止因疾病进展而导致的视力丧失。黄斑厚度在视网膜上的位置的6 $\times$ 6网格上变化，并且在每次访问时由成像过程产生额外的可变性。目前，眼科医生使用重复简单线性回归来估计每个受试者和位置的斜率。为了更精确地估计斜率，我们开发了一种新的贝叶斯分层模型，用于多个受试者，具有空间变化的人口水平和受试者水平系数，借用受试者和测量位置的信息。我们增加了访问效应的模型，以考虑到观察到的空间相关的访问特定的错误。我们用Matérn交叉协方差函数对空间变化的（a）截距、（b）斜率和（c）对数残差标准差（SD）进行建模。每个边际过程假设一个指数核，具有自己的SD和空间相关矩阵。我们开发了我们的模型，并将其应用于晚期青光眼进展研究的数据。我们发现，包括访问的影响，在模型中减少了预测未来的厚度测量误差，大大提高了模型拟合。
英文摘要：
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$\times$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.
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