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.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS298 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org