Ph.D. Thesis Defense Announcement

Title: Disease Progression Modeling using Multi-Dimensional Continuous-Time Hidden Markov Model

Yu-Ying Liu

School of Interactive Computing
College of Computing
Georgia Institute of Technology
http://www.cc.gatech.edu/~yliu88

Date: Wednesday, August 5, 2015
Time: 11 am - 1 pm
Location: TSRB 222

Committee
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Dr. James M. Rehg (Advisor, School of Interactive Computing, Georgia Tech)
Dr. Aaron Bobick  (School of Interactive Computing, Georgia Tech)
Dr. Irfan Essa  (School of Interactive Computing, Georgia Tech)

Dr. Jimeng Sun (School of Computational Science and Engineering, Georgia Tech)
Dr. Hiroshi Ishikawa (School of Medicine, University of Pittsburgh)

Abstract
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The goal of this thesis is to develop a general tool for disease progression modeling which can handle arbitrary observation times, support a multi-dimensional (M-D) view of progression as the co-evolution of multiple interacting biomarkers, capture complex nonlinear patterns, and provide visualizations that effectively communicate the dynamics of disease to domain experts. The development of an M-D view of disease progression is important since many diseases are characterized by several temporally-evolving processes in structure, function, and biochemical, whose interaction can reveal critical but previously undiscovered mechanism.

The Continuous-time hidden Markov model (CT-HMM) is a useful tool in modeling disease progression based on noisy observations of disease states which arrive at irregular sample times. Unfortunately, the modeling flexibility provided by the CT-HMM comes at the cost of a more complex inference procedure than the standard discrete-time HMM. There is no widely-accepted algorithm for efficient parameter learning in the existing literature, and numerical optimization is often utilized directly in maximum likelihood estimation. This has restricted the use of CT-HMM to small models or to applications that make restrictive assumptions on the state transition timing.

In this thesis, we propose to use CT-HMM with M-D gridded state structure to model disease progression, where each dimension represents the change of one or a set of disease markers. By learning dynamic interactions from longitudinal datasets, progression trajectories and patterns can be explored and visualized in the full spectrum of disease evolution, leading to greater insights into population level behavior, enabling prediction of future progression, and the identification of phenotypes. The development of M-D CT-HMM models for large state spaces requires the development of efficient parameter learning methods.

We present the first complete characterization of Expectation-Maximization (EM)-based learning methods in CT-HMM, which both extends and unifies prior work on continuous-time Markov chain (CTMC) models. We address two technical challenges: the estimation of posterior state probabilities, and the computation of end-state conditioned statistics in a CTMC. We efficiently discretize the estimation of posterior state probabilities into a discrete time-inhomogeneous HMM, and present soft and hard EM algorithms. The benefits and drawbacks of these developed methods are analyzed and experimentally validated relative to the existing literature. For CT-HMM hidden path decoding, we present a novel method for computing the path-conditioned expected state duration, which are useful in trajectory decoding and clustering tasks.

Our M-D CT-HMM methods are evaluated on three real-world datasets from Glaucoma, Alzheimer's disease, and Hypertension, with applications including visualizations of the progression, prediction of future measurements, and trajectory clustering. The visualization results of disease progression provide a novel insight into the global structure of progression, and the prediction results outperform the state-of-the-art method for Glaucoma. Our promising results demonstrate that M-D CT-HMM paired with visualizations can provide insights into disease evolution and support the development of individualized treatment plans, resulting in cost-effective disease management.