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. 2021 May 13;11:10248. doi: 10.1038/s41598-021-88923-z

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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We examined the smoking effect on PAL through the use of permutation testing. This was performed one million times per model. The smoking data label for every participant was randomly assigned and the t-statistic for the main effect of smoking in the whole cohort (A), women only (B), and men only was re-calculated (C). We also conducted permutation tests on the interaction between sex × smoking on PAL (D). Black dashed line indicates the full model results statistic. Results from permutation testing indicate the present results are likely not due to chance.