UCLA

Timely detection of glaucoma progression is imperative to identify eyes for treatment and prevent further loss of vision. Methods to diagnose and monitor progression include routine use of structural and functional tests at multiple locations across the macula, the central part of the retina. Visual field (VF) testing provides functional measures of sensitivity to light while optical coherence tomography imaging gives structural thickness measurements of macular layers. In current practice, physicians assess progression by modeling functional or structural changes over time using simple linear regression (SLR) for each subject-location combination separately. This dissertation motivates and develops Bayesian hierarchical spatial longitudinal models to analyze structural and functional data from multiple subjects, borrowing strength across subjects and locations, to better detect glaucoma progression and predict future observations for individual subjects.

Chapter 1 gives an overview of the study objectives and summarizes the contributions of this dissertation. Chapter 2 presents a novel Bayesian hierarchical spatial longitudinal (HSL) model and compares its performance in estimating macular rates of structural change to the performances of SLR and a conditional autoregressive model. Notably in the simulation study, the HSL model is more than three times as efficient as SLR in estimating local rates of change. To more explicitly model the spatial correlation in intercepts, slopes, and residual standard deviations (SD), Chapter 3 proposes a Bayesian hierarchical model with spatially varying random coefficients and visit effects. A comparison of the model to several nested models lacking different model components demonstrates the benefit of incorporating spatially varying visit effects in improving model fit and reducing prediction error. Chapter 4 extends the spatially varying coefficients approach to model VF data. This model simultaneously accounts for censoring and heteroskedasticity, which are inherent qualities of VF data, and the spatial structure in the data. Chapter 4 highlights the importance of using Gaussian processes with nonstationary covariance functions to better model spatial irregularities in the subject-level intercepts and slopes.