The XL-mHG test for enrichment: Algorithms, bounds, and power

8 The XL-mHG test is a semiparametric test for enrichment in ranked lists with boolean (0/1-valued) entries. It is a generalization of the nonparametric mHG test, designed to provide some control over the kind of enrichment that is being tested for, and to allow a flexible trade-off between the sensitivity and robustness of the test. Here, I describe an improved algorithm to efficiently calculate the XL-mHG p-value p, and discuss upper and lower bounds for p. Furthermore, I perform simulations to show that the mHG test is a significantly more powerful alternative to the Kolmogorov-Smirnov (KS) test for detecting enrichment in scenarios that are frequently encountered in biological applications. An open-source Python/Cython implementation of the XL-mHG test is provided in the xlmhg package, available from PyPI and GitHub (https://github.com/flo-compbio/xlmhg) under an OSI-approved license. 9