An Information Theoretic Framework for Protein Activity Measurement

Nonparametric analytical Rank-based Enrichment Analysis (NaRnEA) is a novel gene set analysis method which leverages an analytical null model derived under the Principle of Maximum Entropy. NaRnEA critically improves over two widely used methods - Gene Set Enrichment Analysis (GSEA) and analytical Rank-based Enrichment Analysis (aREA) - as shown by differential activity measurement of ~2,500 transcriptional regulatory proteins across three cohorts in The Cancer Genome Atlas (TCGA) based on the enrichment of their transcriptional targets in differentially expressed genes. Phenotype-matched proteomic data from the Clinical Proteomic Tumor Analysis Consortium (CPTAC) was used to evaluate measurement accuracy. We show that the sample-shuffling empirical null models leveraged by GSEA and aREA are overly conservative, a shortcoming that is critically addressed by NaRnEAs optimal analytical null model.