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. 2021 Sep 15;22:626. doi: 10.1186/s13063-021-05590-1

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© The Author(s) 2021

Open AccessThis 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. 1 — Percentage of time each pair of centers were randomly allocated to the same group (i.e., Center 1 with Center 2, Center 1 with Center 3, Center 1 with Center 4, ..., Center 71 with Center 72). There were a total of 2556 unique center pairs. A Centers randomly allocated without constraints (i.e., simple randomization) would appear in the same arm approximately 50% of the time. B Constraining on a subset of 11 prognostic baseline characteristics. C Constraining on ten principal components from a Principal Component Analysis. The horizontal dashed lines show center pairs (if any) allocated to the same arm 25% or 75% of the time [41]