  Cancer and healthy cells have distinct distributions of molecular properties
and thus respond differently to drugs. Cancer drugs ideally kill cancer cells
while limiting harm to healthy cells. However, the inherent variance among
cells in both cancer and healthy cell populations increases the difficulty of
selective drug action. Here we propose a classification framework based on the
idea that an ideal cancer drug should maximally discriminate between cancer and
healthy cells. We first explore how molecular markers can be used to
discriminate cancer cells from healthy cells on a single cell basis, and then
how the effects of drugs are statistically predicted by these molecular
markers. We then combine these two ideas to show how to optimally match drugs
to tumor cells. We find that expression levels of a handful of genes suffice to
discriminate well between individual cells in cancer and healthy tissue. We
also find that gene expression predicts the efficacy of cancer drugs,
suggesting that the cancer drugs act as classifiers using gene profiles. In
agreement with our first finding, a small number of genes predict drug efficacy
well. Finally, we formulate a framework that defines an optimal drug, and
predicts drug cocktails that may target cancer more accurately than the
individual drugs alone. Conceptualizing cancer drugs as solving a
discrimination problem in the high-dimensional space of molecular markers
promises to inform the design of new cancer drugs and drug cocktails.

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