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The conditional permutation test for independence while controlling for confounders
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Berrett, Thomas B., Wang, Yi, Barber, Rina Foygel and Samworth, Richard J. (2020) The conditional permutation test for independence while controlling for confounders. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82 (1). pp. 175-197. doi:10.1111/rssb.12340 ISSN 1369-7412.
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Official URL: http://dx.doi.org/10.1111/rssb.12340
Abstract
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables X and Y given a potentially high dimensional random vector Z that may contain confounding factors. The test permutes entries of X non‐uniformly, to respect the existing dependence between X and Z and thus to account for the presence of these confounders. Like the conditional randomization test of Candès and co‐workers in 2018, our test relies on the availability of an approximation to the distribution of X|Z—whereas their test uses this estimate to draw new X‐values, for our test we use this approximation to design an appropriate non‐uniform distribution on permutations of the X‐values already seen in the true data. We provide an efficient Markov chain Monte Carlo sampler for the implementation of our method and establish bounds on the type I error in terms of the error in the approximation of the conditional distribution of X|Z, finding that, for the worst‐case test statistic, the inflation in type I error of the conditional permutation test is no larger than that of the conditional randomization test. We validate these theoretical results with experiments on simulated data and on the Capital Bikeshare data set.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Journal of the Royal Statistical Society: Series B (Statistical Methodology) | ||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||
ISSN: | 1369-7412 | ||||||||
Official Date: | February 2020 | ||||||||
Dates: |
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Volume: | 82 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 175-197 | ||||||||
DOI: | 10.1111/rssb.12340 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 16 November 2020 | ||||||||
Date of first compliant Open Access: | 16 November 2020 |
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