Enhancing Migraine Trigger Surprisal Predictions: A Bayesian Approach to Establishing Prospective Expectations

Objective To extend the application of surprisal theory for predicting migraine attack risk by developing methods to estimate trigger variable likelihood in real time, under conditions of limited personal observation.

Prior work has demonstrated that higher surprisal, a measure quantifying the unexpectedness of a trigger exposure, predicts headache onset over 12 to 24 hours. However, these analyses relied on retrospective expectations of trigger exposure formed after extended data collection. To operationalize surprisal prospectively, Bayesian methods could update expectations dynamically over time.

In a prospective daily diary study of individuals with migraine (N = 104), data were collected over 28 days, including stress, sleep, and exercise exposures. Bayesian models were applied to estimate daily expectations for each variable under uninformative and empirical priors derived from the sample. Stress was modeled using a hurdle-Gamma distribution, sleep using a rounded Normal distribution, and exercise using a Bernoulli distribution. Surprisal was calculated based on the predictive distribution at each time point and compared to static empirical surprisal values obtained after full data collection.

Dynamic Bayesian surprisal values systematically differed from retrospective empirical estimates, particularly early in the observation period. Divergence was larger and more variable under uninformative priors but attenuated over time. Empirically informed priors produced more stable, lower-bias surprisal trajectories. Substantial individual variability was observed across exposure types, especially for exercise behavior.

Prospective surprisal modeling is feasible but highly sensitive to prior specification, especially in sparse data contexts (e.g., a binary exposure). Incorporating empirical or individually informed priors may improve early model calibration, though individual learning remains essential. These methods offer a foundation for real-time headache forecasting and dynamic modeling of brain-environment interactions. Competing Interest Statement The authors have declared no competing interest. Funding Statement The research reported in this publication was supported by the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under award number R01NS113823. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The Institutional Review Board of Mass General Brigham gave ethical approval for this work. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Footnotes Funding: The research reported in this publication was supported by the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under award number R01NS113823. Competing Interests: The authors declare no competing interests. Data Availability The data may be available upon reasonable request to the authors.