Background The seizure-count time series data acquired from three children with refractory epilepsy were used in a statistical modelling analysis designed to provide an explanation for the marked variation in seizure frequency that often occurs over time (over-dispersed Poisson behaviour). This was motivated by an expectation that a better understanding of the spontaneous shifts in seizure-activity that are observed in some cases should reduce the risk of over-treatment caused by inappropriate changes in medication. Methods The analyses were performed using Poisson hidden Markov models (HMMs), both Bayesian and non-Bayesian, implemented using Markov chain Monte Carlo and the expectation-maximisation algorithm, respectively. A defining feature of the models, as applied to epilepsy, is the assumed existence of two or more pathological states, with state-specific Poisson rates, and random transitions between the states. Posterior predictive simulation was used to assess the validity of the Bayesian HMMs. Results The results are presented in the form of state transition probability and Poisson rate estimates (i.e., the primary HMM parameters), together with information derived from these primary parameters. State-specific mean-duration (sojourn time) estimates and sojourn-time complementary cumulative probability distributions are the main focus. HMM analyses are presented for three children that differed markedly in their seizure behaviour. The first is characterised by an extreme seizure count on one occasion; the second underwent a spontaneous decrease in seizure activity during the observation period; the third seizure-count time trajectory is characterised by a gradual change in mean seizure activity. We show that, despite their considerable differences, each of the observed seizure-count trajectories can be treated adequately using an HMM. Conclusions The study demonstrates that clinically relevant information can be obtained using HM modelling in three cases with markedly different seizure behaviour. The resulting subject-specific statistics provide useful clinical insights which should aid those engaged in clinical decision making.
Hidden Markov and Semi-Markov Models When and Why are These Models Useful for Classifying States in Time Series Data?
