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

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