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. 2024 Apr 22;15:3385. doi: 10.1038/s41467-024-47806-3

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© The Author(s) 2024

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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Fig. 4 — A Cross-Population. B European population. X-axis represents heritability in percentage. Y-axis represents the corresponding heritability estimated in percentage (marginal.effect: marginal effect heritability; current.drinking: gene and current drinking interaction effect heritability; regular.drinking: gene and regular drinking interaction effect heritability; current.smoking: gene and current smoking interaction effect heritability; ever.smoking: gene and ever smoking interaction effect heritability). Marginal effect heritability refers to the heritability estimated through the marginal effect $\hat{α}$ , and interaction effect heritability refers to the heritability estimated through $\hat{α} - \hat{θ} {\hat{β}}_{1}$ . The percentage number displayed on the right side of each bar represents the estimated heritability, and the corresponding 95% confidence interval shown as horizontal error bars. For the marginal effect analysis, the sample size is 1.65 M and 1.32 M for cross-population and European population analysis, respectively. For the interaction effect analysis, the sample size is 134 K and 80 K for cross-population and European population analysis, respectively.