A Mixed Self-Exciting Process to Model Epileptic Seizures

2026-05-21

AI Summary

This study addresses the challenges of modeling individual heterogeneity and seizure clustering in epilepsy by proposing a Bayesian mixture Hawkes process model. For the first time in epilepsy research, this approach jointly integrates a Weibull baseline intensity, self-excitation effects, covariates, and individual random effects. The model effectively distinguishes between background (spontaneous) and triggered seizures, thereby avoiding the underestimation of baseline intensity and overestimation of excitation rates that arise when random effects are ignored. Application to the HEP dataset demonstrates that the model accurately captures inter-individual variability and seizure cluster characteristics, estimating an average cluster size of 2.20 seizures with a typical interval of approximately 1.57 days between primary and subsequent events. These results underscore the model’s superior performance and clinical interpretability in analyzing event-time data in epilepsy.

Abstract

Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a process we call seizure clustering. Motivated by seizure diary data collected over three years from 407 individuals newly diagnosed with focal epilepsy in the Human Epilepsy Project (HEP), we propose a Bayesian mixed Hawkes process model that addresses seizure clustering and heterogeneity between individuals. In the Hawkes process, the intensity is accelerated each time an event occurs, through the composition of background and excitation intensity functions. The proposed model incorporates a Weibull baseline intensity to model a trend in background seizure rates over time, while the excitation process accounts for seizure clustering within individuals. We model heterogeneity among individuals by including covariates and random effects in both the background and excitation intensities. In the HEP study, the average time between primary and secondary seizures within an individual is 1.57 (95\% CrI: 1.43, 1.70) days, with an average of 2.20 (1.96, 2.47) seizures per cluster. We demonstrate that omitting random effects in the presence of heterogeneity leads to underestimation of the background intensity and overestimation of excitation rates.

Problem

• epileptic seizures
• seizure clustering
• heterogeneity
• Hawkes process
• temporal dynamics

Innovation

• Hawkes process
• seizure clustering
• Bayesian mixed model
• Weibull baseline intensity
• random effects