Unlocking multidimensional cancer therapeutics using geometric data science

Personalised approaches to cancer therapeutics primarily involve identification of patient sub-populations most likely to benefit from targeted drugs. Such a stratification has led to plethora of designs of clinical trials that are often too complex due to the need for incorporating biomarkers and tissue types. Many statistical methods have been developed to address these issues; however, by the time such methodology is available research in cancer has moved on to new challenges and therefore in order to avoid playing catch-up it is necessary to develop new analytic tools alongside. One of the challenges facing cancer therapy is to effectively and appropriately target multiple therapies for sensitive patient population based on a panel of biomarkers across multiple cancer types, and matched future trial designs. We present novel geometric methods (mathematical theory of hypersurfaces) to visualise complex cancer therapeutics data as multidimensional, as well as geometric representation of oncology trial design space in higher dimensions. The hypersurfaces are used to describe master protocols, with application to a specific example of a basket trial design for melanoma, and thus setup a framework for further incorporating multi-omics data as multidimensional therapeutics.