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The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach tomodeling disease progression due to its ability to describe noisy observationsarriving irregularly in time. However, the lack of an efficient parameterlearning algorithm for CT-HMM restricts its use to very small models orrequires unrealistic constraints on the state transitions. In this paper, wepresent the first complete characterization of efficient EM-based learningmethods for CT-HMM models, as well as the first solution to decoding theoptimal state transition sequence and the corresponding state dwelling time. Weshow that EM-based learning consists of two challenges: the estimation ofposterior state probabilities and the computation of end-state conditionedstatistics. We solve the first challenge by reformulating the estimationproblem as an equivalent discrete time-inhomogeneous hidden Markov model. Thesecond challenge is addressed by adapting three distinct approaches from thecontinuous time Markov chain (CTMC) literature to the CT-HMM domain.Additionally, we further improve the efficiency of the most efficient method bya factor of the number of states. Then, for decoding, we incorporate astate-of-the-art method from the (CTMC) literature, and extend the end-stateconditioned optimal state sequence decoding to the CT-HMM case with thecomputation of the expected state dwelling time. We demonstrate the use ofCT-HMMs with more than 100 states to visualize and predict disease progressionusing a glaucoma dataset and an Alzheimer's disease dataset, and to decode andvisualize the most probable state transition trajectory for individuals on theglaucoma dataset, which helps to identify progressing phenotypes in acomprehensive way. Finally, we apply the CT-HMM modeling and decoding strategyto investigate the progression of language acquisition and development.

Efficient Learning and Decoding of the Continuous-Time Hidden Markov Model for Disease Progression Modeling