Disease Progression Modeling Using Multi-Dimensional Continuous-Time Hidden Markov Model
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Continuous-Time Hidden Markov Model (CT-HMM) is a useful tool for modeling disease progression from noisy observed data arriving irregularly in time. However, the lack of any widely-accepted efficient learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic assumptions about the state transition timing. In this dissertation, we present the first complete characterization of EM-based learning methods for CT-HMM models, which involves two challenges: estimation of posterior state probabilities, and the computation of end-state conditioned statistics in a continuous-time Markov chain. We formulate the estimation of posterior state probabilities at observation times as an inference problem in a discrete time-inhomogeneous hidden Markov model, and we present two approaches using either the forward-backward algorithm or Viterbi decoding. Both versions are analyzed and compared against three recent approaches for efficiently computing the end-state conditioned statistics. The proposed EM methods are validated and compared using simulated and real-world datasets. The problem of end-state conditioned optimal state chain decoding is also discussed. We derive a new closed-form solution to calculate the path- and time-conditioned expected state duration which has better time complexity than alternative methods. Finally, we demonstrate the use of CT-HMM to visualize and predict future disease measurements using three datasets in the domains of glaucoma, Alzheimer’s disease, and hypertension. Our visualization results corroborate findings from the recent literature regarding the pattern of progression of these diseases. For a glaucoma prediction task, we show that CT-HMM outperforms the prior state-of-the-art method, Bayesian regression.