  Adaptive therapy is a dynamic cancer treatment protocol that updates (or
"adapts") treatment decisions in anticipation of evolving tumor dynamics. This
broad term encompasses many possible dynamic treatment protocols of
patient-specific dose modulation or dose timing. Adaptive therapy maintains
high levels of tumor burden to benefit from the competitive suppression of
treatment-sensitive subpopulations on treatment-resistant subpopulations. This
evolution-based approach to cancer treatment has been integrated into several
ongoing or planned clinical trials, including treatment of metastatic castrate
resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the
previous few decades, experimental and clinical investigation of adaptive
therapy has progressed synergistically with mathematical and computational
modeling. In this work, we discuss 11 open questions in cancer adaptive therapy
mathematical modeling. The questions are split into three sections: 1) the
necessary components of mathematical models of adaptive therapy 2) design and
validation of dosing protocols, and 3) challenges and opportunities in clinical
translation.
