Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Improved Techniques for Acquisition and Analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging for Detecting Vascular Permeability in the Central Nervous System

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive technique for quantitative assessment of the integrity of blood-brain barrier and blood-spinal cord barrier (BSCB) in the presence of central nervous system pathologies. However, the results of DCE-MRI show substantial variability. The high variability can be caused by a number of factors including inaccurate T1 estimation, insufficient temporal resolution and poor contrast-to-noise ratio. My thesis work is to develop improved methods to reduce the variability of DCE-MRI results. To obtain fast and accurate T1 map, the Look-Locker acquisition technique was implemented with a novel and truly centric k-space segmentation scheme. In addition, an original multi-step curve fitting procedure was developed to increase the accuracy of T1 estimation. A view sharing acquisition method was implemented to increase temporal resolution, and a novel normalization method was introduced to reduce image artifacts. Finally, a new clustering algorithm was developed to reduce apparent noise in the DCE-MRI data. The performance of these proposed methods was verified by simulations and phantom studies. As part of this work, the proposed techniques were applied to an in vivo DCE-MRI study of experimental spinal cord injury (SCI). These methods have shown robust results and allow quantitative assessment of regions with very low vascular permeability. In conclusion, applications of the improved DCE-MRI acquisition and analysis methods developed in this thesis work can improve the accuracy of the DCE-MRI results.