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. 2021 Mar 30;11:7206. doi: 10.1038/s41598-021-86667-4

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© The Author(s) 2021

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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Longitudinal trajectories from bivariate dual change score models, showing change in BMI and cognitive abilities with and without the bivariate coupling-parameter. Trajectories from the full coupling model are shown in black, and those from the no-coupling model in grey. Models were adjusted for sex and education, and a breakpoint in the proportional change parameter added at age 70 for BMI and mental status, and at 65 for episodic memory and total cognition.