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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