  Correct classification of breast cancer sub-types is of high importance as it
directly affects the therapeutic options. We focus on triple-negative breast
cancer (TNBC) which has the worst prognosis among breast cancer types. Using
cutting edge methods from the field of robust statistics, we analyze Breast
Invasive Carcinoma (BRCA) transcriptomic data publicly available from The
Cancer Genome Atlas (TCGA) data portal. Our analysis identifies statistical
outliers that may correspond to misdiagnosed patients. Furthermore, it is
illustrated that classical statistical methods may fail in the presence of
these outliers, prompting the need for robust statistics. Using robust sparse
logistic regression we obtain 36 relevant genes, of which ca. 60\% have been
previously reported as biologically relevant to TNBC, reinforcing the validity
of the method. The remaining 14 genes identified are new potential biomarkers
for TNBC. Out of these, JAM3, SFT2D2 and PAPSS1 were previously associated to
breast tumors or other types of cancer. The relevance of these genes is
confirmed by the new DetectDeviatingCells (DDC) outlier detection technique. A
comparison of gene networks on the selected genes showed significant
differences between TNBC and non-TNBC data. The individual role of FOXA1 in
TNBC and non-TNBC, and the strong FOXA1-AGR2 connection in TNBC stand out. Not
only will our results contribute to the breast cancer/TNBC understanding and
ultimately its management, they also show that robust regression and outlier
detection constitute key strategies to cope with high-dimensional clinical data
such as omics data.
