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. 2020 Sep 11;21:232. doi: 10.1186/s13059-020-02026-y

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© The Author(s) 2020

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/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 2 — Type I error control and power in hypothesis testing of causal relationships by various methods in TWAS. The left panel shows the QQ-plot of testing p values as the simulated data are specifically generated from the null scenario. All methods properly control the type I errors. The right panel shows the receiver operating characteristic (ROC) curves by different methods when the simulated data are from a mixture of null and alternative scenarios. At any specified value of the false-positive rate, PTWAS shows the highest true-positive rate among compared methods. All methods utilizing multiple independent eQTLs show higher powers than SMR (which uses a single best eQTL of each gene as the corresponding instrument)