Fig. 1

Schematic overview of the treeclimbR algorithm. a Data aggregation. An example tree of entities with 10 leaves (1–10) and 9 internal nodes (11–19). Measurements of entities in samples across multiple groups (e.g., Group A, Group B) are shown in the heatmap. For internal nodes, data is generated from their descendant leaves (e.g., node 14 from nodes 2, 3, 4, and 5). Signal branches are colored in blue (higher in Group A) and orange (higher in Group B). b Differential analysis is run on each node to estimate its direction of change and obtain a P value. c The generation of four example candidates, C1,C2,C3 and C4. The climbing starts from the root and stops when reaching leaves or nodes with U=1, a score dependent on a tuning parameter t. d Multiple testing correction on each candidate. Nodes labelled by \(\bigoplus \) are termini (i.e., candidates) obtained in c. C1 is the leaf level where differential analysis is performed when a tree is not available. The null hypothesis is tested on each node of a candidate, and multiplicity is corrected within a candidate. Rejected nodes are shown in red rectangles. e Results from c are summarized in the left table. m, R, and R_L are the number of hypothesis tests (nodes with \(\bigoplus \)), the number of rejected nodes, and the number of rejected leaves (the descendant leaves of rejected nodes), respectively. The best candidate is selected based on three criteria. Candidates that fail in one criterion would not enter to the next. Note: tree notations used in this article are listed below a