In epilepsy, unpredictability of seizures is reported by both patients and clinicians as one of the most debilitating aspects of the disease. Currently, clinicians heavily rely on raw seizure counts to estimate disease risk. However, seizure counts have a tendency to fluctuate on a day-to-day basis due to both natural variation and complex temporal dynamics and thus are an inaccurate proxy for seizure risk. In this thesis, we contribute to research in epilepsy by developing several novel statistical approaches to (1) model neural count data, (2) analyze clinical factors contributing to seizure risk, and (3) forecast seizure risk across days.

First, we introduce a Bayesian non-homogeneous hidden Markov model for unsupervised clustering of zero-inflated seizure count data. Our approach uses a flexible zero-inflated negative binomial emission distribution to account for a high proportion of zeros and/or overdispersion in the data. It also incorporates exogenous covariates into the estimation of the transition and emission probabilities, to allow for inference on factors affecting seizure risk. Implementation follows a Metropolis-within-Gibbs sampler and leverages modern data augmentation methods for efficient sampling and stochastic search methods for automatic variable selection. After assessing performance and sensitivity through simulation studies, we illustrate the clinical utility of the model through an application to daily seizure count data from Seizure Tracker, an electronic seizure diary. We also use the model to analyze the effectiveness of stimulation parameters in patients implanted with a responsive neurostimulation device.

Second, we introduce a physiologically-motivated Bayesian switching linear dynamical system for estimating latent seizure cycles and attractor states within epilepsy. Two types of latent states are introduced to flexibly model the seizure generating process: a discrete attractor state, which captures paroxymal transitions between different levels of seizure risk, and a continuous latent state, which allows for subtle fluctuations in risk conditional on the underlying attractor state. We couple inferences from this model, which utilizes particle Gibbs with ancestral sampling and recursive computing for efficient sampling, with additional statistical post-processing including spectral analysis, signal processing, unsupervised clustering, and analysis of variance, to compare seizure cycling behaviors among different subgroups of patients from Seizure Tracker.

Finally, we develop a natural extension of our proposed state-space model for the problem of forecasting seizure counts in real time. We demonstrate superior performance of the proposed approach over traditional count forecasting methods and consider an application to electrographic seizure counts in patients implanted with a responsive neurostimulation device. Our approach achieves improved performances over chance in a held-out validation set for the majority of patients and across forecast horizons ranging from one to seven days ahead.