Workflow for confirming prognostic, state-of-the-art markers.

(A) We collected data from non-relapsing (NR) and relapsing (R) patients containing 16 immunophenotypic (IPT) markers. (B) To reduce the dimensionality of the data and enable TDA computations, we first selected a subset of markers that contribute most to differences in the shape of the data between the R and NR groups. (C) We constructed pairwise projections of the selected IPT markers in line with standard clinical practice. (D) We applied PH to each patient point cloud, and quantified connected components and loops in the data. (E) For each pairwise combination of IPT markers associated with a particular patient, we computed an 8-dimensional feature vector summarising information from the PH analysis. (F) We applied Random Forest classification to the feature vectors and confirmed that the biomarkers CD10, CD20, CD8 and CD45 contain information that is most relevant for distinguishing R from NR patients based on the shape of their data.