inGSEA: An Improved Method for Gene Set Enrichment Analysis Using a Weighted Integral Statistic

Gene Set Enrichment Analysis (GSEA) is one of the most popular methods for transcriptomic analysis, yet its statistical power is limited when the biological pathways exhibit heterogeneous or non-concordant expression patterns. We propose an improved GSEA method, textbf{in}tegral-based GSEA (inGSEA). inGSEA introduces a novel enrichment score based on the Anderson-Darling weighted integral statistic. The new enrichment score enhances detection power for complex signals, particularly sparse and bidirectional ones, while the Cauchy combination of integral and classic maximum statistics provides robustness across diverse expression patterns. Extensive numerical studies demonstrate that inGSEA achieves superior power and well-calibrated false discoveries. Application to real-world datasets reveals biologically relevant pathways missed by the standard GSEA. inGSEA reduces the computational burden of permutation testing by employing a generalized gamma distribution to approximate the null distribution. inGSEA is accessible as a user-friendly web-based software tool (https://amss-stat.github.io/inGSEA).