Moment based gene set tests
  {\bf Motivation:} Permutation-based gene set tests are standard approaches for testing relationshi ps between collections of related genes and an outcome of interest in high throughput expression analyses. Using $M$ random permutations, one can attain $p$-values as small as $1/(M+1)$. When many gene sets are tested, we need smaller $p$-values, hence larger $M$, to achieve significance while accounting for the n umber of simultaneous tests being made. As a result, the number of permutations to be done rises along with the cost per permutation. To reduce this cost, we seek parametric approximations to the permutation distributions for gene set tes ts.   {\bf Results:} We focus on two gene set methods related to sums and sums of squared $t$ statistics. Our approach calculates exact relevant moments of a weighted sum of (squared) test statistics under permutation. We find moment-based gene set enrichment $p$-values that closely approximate the permutation method $p$-values. The computational cost of our algorithm for linear statistics is on the order of doing $|G|$ permutations, where $|G|$ is the number of genes in set $G$. For the quadratic statistics, the cost is on the order of $|G|^2$ permutations which is orders of magnitude faster than naive permutation. We applied the permutation approximation method to three public Parkinson's Disease expression datasets and discovered enriched gene sets not previously discussed. In the analysis of these experiments with our method, we are able to remove the granularity effects of permutation analyses and have a substantial computational speedup with little cost to accura cy.   {\bf Availability:} Methods available as a Bioconductor package, npGSEA (www.bioconductor.org).   {\bf Contact:} {larson.jessica@gene.com} \end{abstract} 
Jessica L. Larson and Art B. Owen
stat.CO q-bio.QM