Parallelized calculation of permutation tests.

Markus Ekvall,Michael Höhle,Lukas Käll,Pier Luigi Martelli

doi:10.1093/bioinformatics/btaa1007

Abstract

MotivationPermutation tests offer a straightforward framework to assess the significance of differences in sample statistics. A significant advantage of permutation tests are the relatively few assumptions about the distribution of the test statistic are needed, as they rely on the assumption of exchangeability of the group labels. They have great value, as they allow a sensitivity analysis to determine the extent to which the assumed broad sample distribution of the test statistic applies. However, in this situation, permutation tests are rarely applied because the running time of naïve implementations is too slow and grows exponentially with the sample size. Nevertheless, continued development in the 1980s introduced dynamic programming algorithms that compute exact permutation tests in polynomial time. Albeit this significant running time reduction, the exact test has not yet become one of the predominant statistical tests for medium sample size. Here, we propose a computational parallelization of one such dynamic programming-based permutation test, the Green algorithm, which makes the permutation test more attractive.ResultsParallelization of the Green algorithm was found possible by non-trivial rearrangement of the structure of the algorithm. A speed-up—by orders of magnitude—is achievable by executing the parallelized algorithm on a GPU. We demonstrate that the execution time essentially becomes a non-issue for sample sizes, even as high as hundreds of samples. This improvement makes our method an attractive alternative to, e.g. the widely used asymptotic Mann-Whitney U-test.Availabilityand implementationIn Python 3 code from the GitHub repository https://github.com/statisticalbiotechnology/parallelPermutationTest under an Apache 2.0 license.Supplementary information Supplementary data are available at Bioinformatics online.

Highlights

Permutation tests are frequently used for non-parametric testing and are incredibly valuable within computational biology, with applications within genome-wide association studies [16, 1, 4], Pathway Analysis [20, 11], and expression quantitative trait loci studies [3, 21]
We found that the calibration of the parallel Green method was on par with the test
Statistical testing is the base for most scientific activities

Summary

Introduction

Permutation tests are frequently used for non-parametric testing and are incredibly valuable within computational biology, with applications within genome-wide association studies [16, 1, 4], Pathway Analysis [20, 11], and expression quantitative trait loci studies [3, 21]. A way to perform the test is to determine how extreme the observed sum of sample xA, sobs =. XAi is under null hypothesis H0 : μA = μB Both null and alternative hypotheses assume a particular parametric family of distributions, parametrized by their respective mean parameters. The test computes the p value, as the probability of observing sobs or a more extreme value in the alternative’s direction under the assumption that the null-hypothesis is true. A permutation test approach to the testing problem is to assume instead that the labels A and B are exchangeable under H0, as long as they stem from distributions only different in their mean parameters [10] and calculate how frequently samples with sample sums greater or equal than sobs appears when resampling from x

Methods

Results

Conclusion