  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.
