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. 2023 Sep 7;42(7):1133–1149. doi: 10.1038/s41587-023-01934-1

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© The Author(s) 2023

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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Extended Data Fig. 7 — a,b, Bar plots of the Adjusted Rand Index (ARI) of vertically integrated multi-omics datasets of different quality datasets (a, Bad vs. Good) and different scenarios (b, Confounded vs. Balanced) at absolute level (Blue) and ratio level (Red) using SNF, iClusterBayes, MOFA + , MCIA, and intNMF. Data of each omics type were preprocessed by Absolute (no further processing on the normalized datasets), Ratio, ComBat, Harmony, RUVg, or Z-score for horizontal integration. The number of data sampling and integration instances (n) used to derive statistics were as follows: Bad, n = 10; Good, n = 10; Confounded, n = 200; Balanced, n = 100. Data are presented as mean values ± SD. c, Scatter plots between ARI between predicted labels and batches as well as the degree of sample class-batch balance with different data preprocessing methods. Each point represents an instance of data sampling and integration. The solid lines depict local regression fit of the data and shaded regions depict 95% confidence intervals.