Enrichment on steps, not genes, improves inference of differentially expressed pathways

Enrichment analysis is frequently used in combination with differential expression data to investigate potential commonalities amongst lists of genes and generate hypotheses for further experiments. However, current enrichment analysis approaches on pathways ignore the functional relationships between genes in a pathway, particularly OR logic that occurs when a set of proteins can each individually perform the same step in a pathway. As a result, these approaches miss pathways with large or multiple sets because of an inflation of pathway size (when measured as the total gene count) relative to the number of steps. We address this problem by enriching on step-enabling entities in pathways. We treat sets of protein-coding genes as single entities, and we also weight sets to account for the number of genes in them using the multivariate Fisher's noncentral hypergeometric distribution. We then show three examples of pathways that are recovered with this method and find that the results have significant proportions of pathways not found in gene list enrichment analysis.