Collaborative Research: Stochastic and Dynamic Chemotherapy Planning and Dosing

该奖项将通过开发在不确定性下多个时间段内安排和给药化疗的新方法，为国家繁荣和经济福利的发展做出贡献。化疗是三种最常见的癌症治疗方法之一，但很少有方法考虑其最佳用途。该奖项将开发几种创新技术，因为它研究表征响应和剂量的动态方法。该研究整合了连续和离散的决策。 一个这样的方面考虑时间：癌症和化疗药物随着时间的推移不断变化，但给药决策发生在离散的时间段（即医生预约）。另一个这样的方面考虑剂量决定;化疗药物通常通过药丸给予，这限制了剂量选择。这些新的模型提出了强大的建模和计算的挑战。这个奖项的目标是符合国家科学基金会的使命目标，促进提高国民健康。 该奖项将通过莱斯大学的各种项目涉及来自代表性不足群体的学生。这项研究将开发一个新的框架，以建立下一代模型，用于随着时间的推移和不确定性下的化疗计划和剂量决策。一个主要的挑战是确定如何在时间和决策方面融合问题的连续和离散方面。该项目的框架融合了常微分方程和随机混合整数规划。与以前的方法不同，该框架允许将各种剂量和毒性限制作为随机混合整数规划内的线性约束。许多控制肿瘤生长的微分方程只能近似求解，因此本研究的一个主要目标是了解近似和误差界限如何在模型中集成。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This award will contribute to the advancement of national prosperity and economic welfare by developing novel methods for scheduling and dosing chemotherapy over multiple time periods under uncertainty. Chemotherapy is one of the three most common cancer therapies, yet few methods have considered its optimal use. This award will develop several innovative techniques as it studies dynamic methods of characterizing response and dosage. The research integrates both continuous and discrete decisions. One such aspect considers time: cancer and chemotherapy drugs change continuously over time, but dosing decisions occur at discrete time periods (i.e. doctor appointments). Another such aspect considers dosing decisions; chemotherapy drugs are often given via pills, which limits dosing options. These novel models present formidable modeling and computational challenges. The goals of this award are in line with the NSF mission goal of promoting the enhancement of national health. This award will involve students from under-represented groups through various programs at Rice University.This research will develop a novel framework to build next-generation models for chemotherapy scheduling and dosing decisions over time and under uncertainty. A major challenge is in determining how to blend continuous and discrete aspects of the problem in terms of time and decisions. The project's framework blends ordinary differential equations and stochastic mixed-integer programming. Unlike previous approaches, this framework allows the inclusion of various dosing and toxicity restrictions as linear constraints within the stochastic mixed-integer program. Many of the differential equations governing tumor growth can only be solved approximately, so a major goal of this research is to understand how approximations and error bounds can be integrated across the models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.