Statistics – Applications
Scientific paper
2010-11-10
Annals of Applied Statistics 2010, Vol. 4, No. 2, 1014-1033
Statistics
Applications
Published in at http://dx.doi.org/10.1214/09-AOAS298 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins
Scientific paper
10.1214/09-AOAS298
Permutation $p$-values have been widely used to assess the significance of linkage or association in genetic studies. However, the application in large-scale studies is hindered by a heavy computational burden. We propose a geometric interpretation of permutation $p$-values, and based on this geometric interpretation, we develop an efficient permutation $p$-value estimation method in the context of regression with binary predictors. An application to a study of gene expression quantitative trait loci (eQTL) shows that our method provides reliable estimates of permutation $p$-values while requiring less than 5% of the computational time compared with direct permutations. In fact, our method takes a constant time to estimate permutation $p$-values, no matter how small the $p$-value. Our method enables a study of the relationship between nominal $p$-values and permutation $p$-values in a wide range, and provides a geometric perspective on the effective number of independent tests.
Sun WaiChing
Wright Fred A.
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