A robust optimization approach to cancer treatment under toxicity uncertainty

Junfeng Zhu, Hamidreza Badri, Kevin Leder

Research output: Chapter in Book/Report/Conference proceedingChapter


The design of optimal protocols plays an important role in cancer treatment. However, in clinical applications, the outcomes under the optimal protocols are sensitive to variations of parameter settings such as drug effects and the attributes of age, weight, and health conditions in human subjects. One approach to overcoming this challenge is to formulate the problem of finding an optimal treatment protocol as a robust optimization problem (ROP) that takes parameter uncertainty into account. In this chapter, we describe a method to model toxicity uncertainty. We then apply a mixed integer ROP to derive the optimal protocols that minimize the cumulative tumor size. While our method may be applied to other cancers, in this work we focus on the treatment of chronic myeloid leukemia (CML) with tyrosine kinase inhibitors (TKI). For simplicity, we focus on one particular mode of toxicity arising from TKI therapy, low blood cell counts, in particular low absolute neutrophil count (ANC). We develop optimization methods for locating optimal treatment protocols assuming that the rate of decrease of ANC varies within a given interval. We further investigated the relationship between parameter uncertainty and optimal protocols. Our results suggest that the dosing schedule can significantly reduce tumor size without recurrence in 360 weeks while insuring that toxicity constraints are satisfied for all realizations of uncertain parameters.

Original languageEnglish (US)
Title of host publicationMethods in Molecular Biology
PublisherHumana Press Inc.
Number of pages35
StatePublished - 2018

Publication series

NameMethods in Molecular Biology
ISSN (Print)1064-3745

Bibliographical note

Funding Information:
JZ was supported by NSF grant DMS-1224362. HB was supported by NSF grant CMMI-1362236. KL was supported by NSF grants CMMI-1362236 and CMMI-1552764.

Publisher Copyright:
© 2018, Springer Science+Business Media LLC.


  • Cancer treatment
  • Mixed integer optimization
  • Robust optimization
  • Toxicity uncertainty


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