A Markov chain method for counting and modelling migraine attacks

To ensure reproducibility in research quantifying episodic migraine attacks, and identifying attack onset, a sound theoretical model of a migraine attack, paired with a uniform standard for counting them, is necessary. Many studies report on migraine frequencies—e.g. the fraction of migraine-days of the observed days—without paying attention to the number of discrete attacks. Furthermore, patients’ diaries frequently contain single, migraine-free days between migraine-days, and we argue here that such ‘migraine-locked days’ should routinely be interpreted as part of a single attack. We tested a simple Markov model of migraine attacks on headache diary data and estimated transition probabilities by mapping each day of each diary to a unique Markov state. We explored the validity of imputing migraine days on migraine-locked entries, and estimated the effect of imputation on observed migraine frequencies. Diaries from our patients demonstrated significant clustering of migraine days. The proposed Markov chain model was shown to approximate the progression of observed migraine attacks satisfactorily, and imputing on migraine-locked days was consistent with the conceptual model for the progression of migraine attacks. Hence, we provide an easy method for quantifying the number and duration of migraine attacks, enabling researchers to procure data of high inter-study validity.