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

• Published in: Journal of the American Statistical Association Vol. 114; no. 526; pp. 495 - 513
• Main Authors: Lee, Wonyul, Miranda, Michelle F., Rausch, Philip, Baladandayuthapani, Veerabhadran, Fazio, Massimo, Downs, J. Crawford, Morris, Jeffrey S.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 03.04.2019; Taylor & Francis Group, LLC; Taylor & Francis Ltd
• Subjects: Age; Age differences; Applications and Case Studies; autocorrelation; Bayesian analysis; Bayesian theory; Biomechanics; Blindness; Correlation; Damage assessment; Etiology; eyes; Functional data analysis; Functional mixed models; Functional regression; Functionals; Glaucoma; growth curves; Hypotheses; Intraocular pressure; Longitudinal functional data; nerve tissue; Nonparametric effects; Nonparametric statistics; Regression analysis; risk; Risk analysis; Risk factors; Smoothing splines; Smoothness; Statistical inference; Statistical methods; Statistics; Transformation; Bayesian models; Glaucoma; Smoothing Splines; Wavelets; Functional regression; Longitudinal Functional Data; Nonparametric effects; Spherical data; Functional mixed models; Functional data analysis
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2018.1476242

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. Supplementary materials for this article are available online.