Quickest Way to Less Headache Days: an operational research model and its implementation for Chronic Migraine

Abstract

Structured AbstractBackgroundChoosing migraine prevention medications often involves trial and error. Operations research methodologies, however, allow us to derive a mathematically optimum way to conduct such trial and error processes.ObjectiveGiven probability of success (defined as 50% reduction in headache days) and adverse events as a function of time, we seek to develop and solve an operations research model, applicable to any arbitrary patient, minimizing time until discovery of an effective migraine prevention medication. We then seek to apply our model to real life data for chronic migraine prevention.MethodsWe develop a model as follows: Given a set of D many preventive medications, for drug i in D, we describe the likelihood of reaching 50% headache day reduction over the course of time, (ti,1 ≤ ti,2 ≤ …) by probability (pi,1 ≤ pi,2 ≤ …). We additionally assume a probability of adverse event(qi,1 ≤ qi,2 ≤ …). We then solve for a sequence of prescription trials that minimizes the expected time until an effective drug is identified.Once we identify the optimal sequence for our model, we estimate p, t and q for topiramate and OnabotulinumtoxinA based on the FORWARD study by Rothrock et al as well as erenumab data published by Barbanti et al. at IHC 2019.ResultsThe solution for our model is to order the drugs by probability of efficacy per unit time. When the efficacy of each drug i is known only for one period ti and there are no adverse effects, then the optimum sequence is to administer drug i for ti periods in decreasing order pi/ti. In general, the optimum sequence is to administer drug i for ti,k* periods in decreasing order of the Gittins index σi,k*Based on the above data, the optimum sequence of chronic migraine prevention medication is a trial of erenumab for 12 weeks, followed by a trial of OnabotulinumtoxinA for 32 weeks, followed by a trial of topiramate for 32 weeks.ConclusionWe propose an optimal sequence for preventive medication trial for patients with chronic migraine. Since our model makes limited assumptions on the characteristics of disease, it can be readily applied also to episodic migraine, given the appropriate data as input.Indeed, our model can be applied to other scenarios so long as probability of success/adverse event as a function of time can be estimated. As such, we believe our model may have implications beyond our sub-specialty.Trial RegistrationNot applicable.