Collaborative Research: Stochastic and Dynamic Chemotherapy Planning and Dosing

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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.