Unfortunately, the additional modeling flexibility provided by CT-HMM comes at the cost of a more complex inference procedure. It is therefore suitable for irregularly-sampled temporal data such as clinical measurements.
However, in reality patient visits are irregular in time, as a consequence of scheduling issues, missed visits, and changes in symptomatology.Ī Continuous-Time HMM (CT-HMM) is an HMM in which both the transitions between hidden states and the arrival of observations can occur at arbitrary (continuous) times. While conventional hidden Markov models (HMMs) have been used to model disease progression, they are not suitable in general because they assume that measurement data is sampled regularly at discrete intervals. Hidden variable models are particularly attractive for modeling disease progression for three reasons: 1) they support the abstraction of a disease state via the latent variables 2) they can deal with noisy measurements effectively and 3) they can easily incorporate dynamical priors and constraints. Furthermore, progression models can support phenotyping by providing a natural similarity measure between trajectories which can be used to group patients based on their progression. In addition, the models can be used to predict the future course of disease in an individual, supporting the development of individualized treatment schedules and improved treatment efficiencies. By distilling population data into a compact representation, disease progression models can yield insights into the disease process through the visualization and analysis of disease trajectories. The goal of disease progression modeling is to learn a model for the temporal evolution of a disease from sequences of clinical measurements obtained from a longitudinal sample of patients. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset.
The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model.
We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time.
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