Weighted Kolmogorov Smirnov testing: an alternative for Gene Set Enrichment Analysis

Gene Set Enrichment Analysis (GSEA) is a basic tool for genomic data treatment. From a statistical point of view, the centering of its test statistic does not allow the derivation of asymptotic results. A test statistic with a different centering is proposed. Under the null hypothesis, the convergence in distribution of the new test statistic is proved, using the theory of empirical processes. The limiting distribution can be computed by Monte-Carlo simulation. The test defined in this way has been called Weighted Kolmogorov Smirnov (WKS) test. The fact that the evaluation of the asymptotic distribution serves for many different gene sets results in shorter computing times. Using expression data from the GEO repository, tested against the MSig Database C2, a comparison between the classical GSEA test and the new procedure has been conducted. Our conclusion is that, beyond its mathematical and algorithmic advantages, the WKS test could be more informative in many cases, than the classical GSEA test.