Topology-Based Biomarkers Accurately Predict Breast Cancer Outcome and Survival.

[UNLABELLED] Loss of organized structure is a hallmark of malignant transformation in breast cancer. Traditionally, such morphologic features are captured by descriptive histologic assessments, such as grade, that represent reliable diagnostic and prognostic determinants. Nonetheless, the predictive value of these semiquantitative approaches is limited by their subjective nature and the computational restrictions inherent to discrete integer-based scoring systems. In this study, we describe an application of topological measurements and statistical modeling to derive continuous mathematical scores that quantitatively reflect the level of organized structure within human breast cancer tissues. This approach generated quantifiable biomarkers, assessable on a continuous scale, that predicted breast cancer survival. Compared with traditional biomarkers, these topology-based measurements showed higher prognostic accuracy with less variation associated with race and ethnicity. Integration of these biomarkers with gene expression data produced topology-derived gene signatures that predicted therapeutic response and uncovered gene regulatory networks linking metabolism with the breast cancer tumor microenvironment in racially diverse breast cancer cohorts. Overall, this study demonstrates the potential of spatial and topological biomarkers in breast cancer treatment and diagnosis. Application and adaptation of methods that quantify tumor architectural features to develop prognostic and predictive algorithms exemplify the immense future promise of defining linkages among biology, medicine, and mathematics.

[SIGNIFICANCE] Topological features of breast cancer histology can be quantified on a continuous scale and used to accurately predict breast cancer patient survival and response to therapy.