Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, with Application to Glaucoma Data

Glaucoma, a leading cause of blindness, is characterized by optic nerve damage related to intraocular pressure (IOP), but its full etiology is unknown. Researchers at UAB have devised a custom device to measure scleral strain continuously around the eye under fixed levels of IOP, which here is used to assess how strain varies around the posterior pole, with IOP, and across glaucoma risk factors such as age. The hypothesis is that scleral strain decreases with age, which could alter biomechanics of the optic nerve head and cause damage that could eventually lead to glaucoma. To evaluate this hypothesis, we adapted Bayesian Functional Mixed Models to model these complex data consisting of correlated functions on spherical scleral surface, with nonparametric age effects allowed to vary in magnitude and smoothness across the scleral surface, multi-level random effect functions to capture within-subject correlation, and functional growth curve terms to capture serial correlation across IOPs that can vary around the scleral surface. Our method yields fully Bayesian inference on the scleral surface or any aggregation or transformation thereof, and reveals interesting insights into the biomechanical etiology of glaucoma. The general modeling framework described is very flexible and applicable to many complex, high-dimensional functional data.

青光眼作为首要致盲性疾病，其特征为与眼内压（intraocular pressure, IOP）相关的视神经损伤，但完整病因迄今尚未明确。UAB的研究人员研发了一款定制化设备，可在固定眼内压水平下持续测量眼球周围的巩膜应变，以此评估巩膜后极部、眼内压水平以及年龄等青光眼危险因素维度下的应变分布变化情况。本研究的假说为：巩膜应变随年龄增长而降低，这可能改变视神经乳头的生物力学特性，进而引发损伤并最终导致青光眼。为验证该假说，我们采用贝叶斯功能混合模型（Bayesian Functional Mixed Models）对复杂数据进行建模：该数据集包含球形巩膜表面上的相关函数数据，允许非参数年龄效应在巩膜表面的幅度与平滑度上存在差异；引入多层随机效应函数以捕捉组内相关性，并设置功能生长曲线项以捕捉巩膜表面不同位置眼内压下的序列相关性。我们的方法可实现巩膜表面或其任意聚合、变换形式下的全贝叶斯推断，并为青光眼的生物力学病因学提供了颇具价值的见解。本文所提出的通用建模框架具有极强的灵活性，可应用于诸多复杂的高维功能型数据场景。