Migraine day frequency in migraine prevention: longitudinal modelling approaches

DOI: https://doi.org/10.1186/s12874- 019- 0664- 5

Abstract-Summary Many clinical trials report outcomes using the frequency of an event over a set period of time, for example, the primary efficacy outcome in most clinical trials of migraine prevention is mean change in the frequency of migraine days (MDs) per 28 days (monthly MDs [MMD]) relative to baseline for active treatment versus placebo.

Parametric models of change in MMD for migraine preventives were assessed

using data from erenumab clinical studies.

For each trial, two longitudinal regression models were fitted: negative binomial

and beta binomial.

Using the erenumab study data, both the negative binomial and beta-binomial models provided unbiased estimates relative to observed trial data with well-fitting distribution at various time points.

This proposed methodology, which has not been previously applied in migraine,

has shown that these models may be suitable for estimating MMD frequency.

Modelling MMD using negative binomial and beta-binomial distributions can be advantageous because these models can capture intra- and inter-patient variability so that trial observations can be modelled parametrically for the purposes of eco- nomic evaluation of migraine prevention.

Background Examining the mean change in MMD frequency across a cohort of patients may not capture the clinically meaningful effects of migraine prevention, such as the

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improvement in an individual’s ability to perform daily activities or health-related quality of life.

It is considered appropriate for unrestricted count data [420], and because MMD frequency is a count variable, Poisson distribution may be considered an eligi- ble model.

A preliminary analysis, based on cross-sections of the data, has indicated that the beta-binomial is an alternative distribution that could be used to model MMD fre- quency data and has been shown to provide comparable fits to the negative binomial models [421].

Longitudinal negative binomial and beta-binomial regression models that accom- modate over-dispersed data have not been used previously in the assessment of MMD frequency.

Methods Three longitudinal regression models were evaluated for their ability to estimate the frequency distribution of MMD: multilevel/hierarchical negative binomial regres- sion (with constant dispersion parameter over time), multilevel beta-binomial regression (with constant ICC over time) and the multilevel Poisson model.

The α and β parameters of the beta-binomial distribution can be calculated from the mean and ICC, which represents the strength of the correlation between days for the same patient, i.e. daily outcomes are likely to be similar for the same patient.

The beta-binomial probability function is specified as follows: Where: k is the number of MDs P (Y = k) is the probability of patients experiencing τ MDs N is the number of days in the cycle (28 days) B () is the beta function α and β are the param- eters of the underlying beta distribution.

This approach allows the regression models to estimate both the change in MMD frequency over time and the dispersion parameters required to reproduce the distri- bution of patient-level MMD frequency.

Results The predicted distributions show a good fit to the actual observations in the EM and CM study; the RMSE estimates were 0.075 and 0.082 for negative binomial regres- sion, 0.102 and 0.081 for beta-binomial regression and 0.142 and 0.152 for Poisson regression for EM and CM studies respectively.

The MAE estimates were 0.246 and 0.330 for negative binomial regression, 0.336 and 0.339 for beta-binomial regression, and 0.466 and 0.654 for Poisson regression for EM and CM studies respectively.

For the EM study, the negative binomial mean MMD for weeks 0, 4, 12 and 24

were 8.261, 7.199, 6.434 and 6.421, respectively.

For the CM study, the negative binomial mean MMD for weeks 0, 4, 8 and 12

were 18.111, 15.418, 14.538 and 13.997, respectively.

Discussion The approaches described here allows the distribution of individual patients by MMD to be modelled using only the clinical endpoint of the studies  - the mean change from baseline in MMD compared with placebo at a single time point.

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The Poisson and negative binomial distributions have been used in previous stud- ies to model count data [422–424] and have also been used to approximate head- ache day frequency data in published migraine studies [425, 426].

Modelling data as continuous events rather than categorising data has many advantages, including the reduction of bias and more accurately estimating the extent of variation in outcomes between groups [427]. This analysis takes the approach of modelling migraine frequency as a continuous outcome and addresses a key limitation of previous modelling approaches which define health states by categorical event frequency or response status.

The proposed approach also provides a greater capability to model indirect com- parisons than previous models, as the published endpoints of clinical studies (i.e. mean change in MMD) can be used to estimate the distributions of patients, assum- ing the patient-level variation is similar across cohorts.

Conclusions Modelling MMD with regression models that can accommodate overdispersion in a longitudinal framework is a statistically valid method to estimate the variation in MMD, both within and between individual patients.

This approach, which estimates the distribution of patients by MMD, allows out- comes (such as health-related quality of life or pain medication use) to be directly quantified and linked to MD frequency.

Acknowledgement A machine generated summary based on the work of Di Tanna, Gian Luca; Porter, Joshua K.; Lipton, Richard B.; Brennan, Alan; Palmer, Stephen; Hatswell, Anthony J.; Sapra, Sandhya; Villa, Guillermo. 2019 in BMC Medical Research Methodology.

Disability, quality of life, productivity impairment and employer costs of migraine in the workplace