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. 2022 Sep 23;12:403. doi: 10.1038/s41398-022-02186-4

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© The Author(s) 2022

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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Genetic correlation forest plot between schizophrenia and SUDs (AD, CUD, ND, and OD), r_g calculated using linkage disequilibrium (LD) score regression. b Latent causal variable (LCV) model to test for partial causality with posterior mean genetic causality proportion (GCP) estimates of each SUD on schizophrenia. Absolute magnitude of the Z-score relates to the test of whether the posterior mean GCP estimate is significantly different than zero. The vertical line represents genetic causality, with a posterior mean GCP > 0.6 implying partial genetic causality of trait 1 and trait 2, and inverse for GCP < −0.6. The horizontal line represents an absolute Z-score of ~1.96, which is nominal uncorrected significance (P < 0.05) for a test of whether GCP value is significantly non-zero.