In the era of precision medicine, cancer therapies are tailored to the specific genetic makeup of a tumour. A main challenge during treatment is the early detection of variations in tumour phenotype that might alter the expected outcome. Early and precise detection of cancer response to treatment is not only important for patient cure success but is also critical to optimise the development of new targeted therapies or other therapeutic strategies. Current evaluation of genomic aberrations using biopsy is not appropriate for treatment follow-up, since procedures are invasive, cannot be frequently repeated and samples may not be representative of the whole lesion.

Radiomics is an emerging area that converts medical imaging data into large amount of multiview measures (imaging phenotype) of the whole tumour correlated with genomics. Although abnormal radiomic features could be predictive early response biomarkers to cancer treatments, there are no methods specifically developed for detection of abnormalities. Detection of abnormal radiomic features should model multi-view spaces with Small Sample Size (SSS) data prone to have a complex manifold structure. Topology is a powerful mathematical approach to model the structure of complex manifolds without the assumption of any parametric model for the data.

TOPiomics is the 1^st imaging technique specific for early detection of variations in tumour imaging phenotype altering the response of anti-cancer treatments. TOPiomics topological description is able to model the complex structure of radiomics SSS multi-view data ensuring reproducible clinical results. Its non-parametric local description endows TOPiomics with high robustness to detect abnormalities in SSS contexts, while its view-sensitive approach allows early detection of abnormal imaging phenotypes. Therefore, TOPiomics is a unique specific technique to define robust imaging biomarkers for outcome in cancer treatment follow-up that will improve cancer patients care by optimising treatment selection and sequence.