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Abstract:
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Researchers in genetics and other life sciences use permutation tests to evaluate differences between groups. Permutation tests have desirable properties, including exactness, and are applicable even when the distribution of the test statistic is analytically intractable. However, permutation tests can be computationally intensive. We propose an algorithm for quickly approximating small permutation p-values in two-sample tests. Our approach is based on a stochastic ordering of test statistics across partitions of the permutation space, which allows us to calculate p-values in partitions that require less computation and then predict p-values in partitions that would require more computation. In this article, we present our method and demonstrate its use through simulations and an application to cancer genomic data. We find that our method is faster than a current leading method, and can successfully identify up- and down-regulated genes. We have implemented our method in the R package fastPerm.
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