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

TL;DR

This paper introduces a Bayesian semiparametric functional mixed model to analyze complex, correlated spherical functional data, specifically applied to scleral strain measurements related to glaucoma risk factors.

Contribution

It develops a flexible Bayesian modeling framework for high-dimensional, correlated functional data on spherical surfaces, incorporating nonparametric effects and multi-level random effects.

Findings

Scleral strain decreases with age, affecting optic nerve biomechanics.

The model provides detailed Bayesian inference on scleral surface data.

Insights into the biomechanical etiology of glaucoma are revealed.

Abstract

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.