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XL-mHG: A Semiparametric Test for Enrichment

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This is an efficient Python/Cython implementation of the semiparametric XL-mHG test for enrichment in ranked lists. The XL-mHG test is an extension of the nonparametric mHG test, which was developed by Dr. Zohar Yakhini and colleagues.

If you use the XL-mHG test in your research, please cite Eden et al. (PLoS Comput Biol, 2007) and Wagner (PeerJ Preprints, 2016).

Installation

$ pip install xlmhg

Usage

import xlmhg
stat, cutoff, pval = xlmhg.xlmhg_test(v, X, L)

Where v is a NumPy array of type "np.uint8" containing only zeros and ones, X, and L are parameters, and the return values have the following meanings:

  • stat: The XL-mHG test statistic

  • cutoff: The cutoff at which the XL-mHG test statistic was attained

  • pval: The XL-mHG p-value

What do the X and L parameters mean?

  • X refers to the minimum number of “1’s” that have to be seen before anything can be called “enrichment”.

  • L is the lowest cutoff (i.e., the largest n) that is being tested for enrichment.

A more direct way to understand X and L is through the definition of the XL-mHG test statistic. It is defined as the minimum hypergeometric p-value over all cutoffs at which at least X “1’s” have already been seen, and which are at or below the n’th cutoff. All other cutoffs are ignored. For X=1 and L=N, no relevant cutoffs are ignored, and the XL-mHG test reduces to the mHG test.

Background

For a discussion of the statistical background and implementation of this test, please see my Technical Report on arXiv, as well as my PeerJ Preprint article.

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