Novel Approaches to Longitudinal Modeling of Migraine Day Frequency

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Migraine is a neurological disorder characterized by recurrent headaches of moderate to severe pain intensity and is a leading cause of long-term disability. In clinical studies of medications used to prevent migraine, an end point used by researchers is the mean change in monthly migraine days (MMD) for the entire study population; however, this end point may not show the effects of preventive treatment on clinically important outcomes, such as health-related quality of life (QOL). Also, the frequency, duration, and severity of migraine headaches vary both from patient to patient and within the same patient, and taking into account this variability is important when modeling the effectiveness and cost-effectiveness of preventive treatment. In addition, the average outcome for a group of patients may not be representative of the outcome for a patient with average MMD. Thus, there is a need for an alternate model to evaluate the change in mean MMD for the full study population, as well as the distribution of individual patients falling into a specific MMD frequency classification at later time points.1

Health economic data are used by reimbursing agencies when evaluating medications; however, these data are frequently derived from short-term clinical studies. Modeling may be useful to evaluate outcomes over a longer time horizon. Previous research has used the Poisson and negative binomial approaches to model MMD frequency. While the Poisson distribution may provide an acceptable model for mean migraine frequency across a group of patients, it may be inadequate for modeling migraine data in an individual patient. The negative binomial approach provides a better match for data from patients with migraine because it takes into account inter- and intrapatient variability, and the beta-binomial approach may provide additional advantages in this patient population due to differences in the way outcomes are classified.1


Erenumab, which is indicated for the prevention of migraine in adults, is a human monoclonal antibody that targets and antagonizes the calcitonin gene—related peptide receptor.2 Using data from 2 clinical studies of erenumab, researchers evaluated how well the Poisson, negative binomial, and beta-binomial approaches modeled changes in MMD frequency and how well the estimated distributions based on these models matched the actual distributions from the studies of erenumab.1



Compared with the Poisson approach, the MMD distributions derived from the negative binomial and beta-binomial approaches were a closer match to the actual data from the clinical studies of erenumab.1


There can be considerable variability both among patients and within the same patient in the frequency, duration, and severity of migraine attacks. The negative binomial and beta-binomial approaches provide a good fit for these types of data, as they better account for variability in the data. In addition, these approaches allow modeling of the patient distribution by MMD frequency, which in turn permits outcomes such as use of pain medication or health-related QOL to be calculated and linked with migraine frequency.1

These modeling approaches can also be used to extrapolate long-term outcomes data based on short-term data from clinical trials. Study authors noted that there is a level of uncertainty associated with extrapolation of outcomes, as a patient’s clinical course can be unpredictable, and that further research is needed in this area because this is a relatively new approach.1


The use of negative binomial and beta-binomial approaches to estimate MMD frequency is statistically valid. Furthermore, these approaches may be used to generate data for the evaluation of medications for migraine prevention.1


1. Di Tanna GL, Porter JK, Lipton RB, et al. Migraine day frequency in migraine prevention: longitudinal modelling approaches. BMC Med Res Methodol. 2019;19(1):20. doi: 10.1186/s12874-019-0664-5.

2. Aimovig [prescribing information]. Thousand Oaks, CA: Amgen, Inc; 2018. Accessed March 1, 2019.