Lo Irene, Zhang Pengfei
Department of Management Science & Engineering, Stanford University, Stanford, CA, USA.
Department of Neurology, Beth Israel Deaconess Medical Center, Boston, MA, USA.
BMC Neurol. 2025 Mar 31;25(1):132. doi: 10.1186/s12883-025-04124-5.
Choosing 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.
Given 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.
An operations research model is developed and then solved for the optimum solution, taking into account the likelihood of reaching 50% headache day reduction as a function of time. We then estimate key variables using FORWARD study by Rothrock et al. as well as erenumab data published by Barbanti et al. at International Headache Congress 2019.
The solution for our model is to order the medications in decreasing order by probability of efficacy per unit time. This result can be generalized through calculation of Gittins index. In the case of chronic migraine 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.
We 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.
选择偏头痛预防药物通常需要反复试验。然而，运筹学方法能让我们得出一种数学上最优的方式来进行这种反复试验过程。
给定成功概率（定义为头痛天数减少50%）以及不良事件随时间的函数关系，我们试图开发并求解一个运筹学模型，该模型适用于任何任意患者，以最小化发现有效偏头痛预防药物所需的时间。然后，我们试图将我们的模型应用于慢性偏头痛预防的实际生活数据。
开发一个运筹学模型，然后求解最优解，同时考虑到头痛天数减少50%的可能性随时间的函数关系。然后，我们使用Rothrock等人的前瞻性研究以及Barbanti等人在2019年国际头痛大会上发表的erenumab数据来估计关键变量。
我们模型的解决方案是按照单位时间内疗效概率从高到低的顺序排列药物。这个结果可以通过计算吉廷斯指数来推广。在慢性偏头痛的情况下，慢性偏头痛预防药物的最优顺序是先试用erenumab 12周，接着试用onabotulinumtoxinA 32周，然后试用托吡酯32周。
我们为慢性偏头痛患者提出了预防性药物试验的最优顺序。由于我们的模型对疾病特征的假设有限，只要有适当的数据作为输入，它也可以很容易地应用于发作性偏头痛。事实上，只要能估计成功概率/不良事件随时间的函数关系，我们的模型就可以应用于其他情况。因此，我们相信我们的模型可能具有超出我们亚专业领域的意义。
