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. 2016 Sep 6;17(1):438. doi: 10.1186/s13063-016-1571-2

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© The Author(s). 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided 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 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.

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Fig. 1 — Association between type I error rate and number of clusters for ‘appropriate’ and ‘inappropriate’ methods of analysis. This figure presents the association between the total number of clusters and the risk of an inflated type I error rate for different methods of analysis. Panels a and b show the type I error rate for methods of analysis that are ‘inappropriate’ to use with a small number of clusters. Panels c and d show the type I error rate for methods of analysis that are ‘appropriate’ to use with a small number of clusters. The mixed-effects models in panels c and d used a Satterthwaite degree-of-freedom correction. The GEE models in panels c and d used the correction proposed by Fay and Graubard. Panels a and c represent a small cluster scenario (e.g. a family). Panels b and d represent a large cluster scenario (e.g. a hospital). The intraclass correlation coefficient (ICC; a measure of how correlated participants within a cluster are) was set as 0.15 for ‘small’ clusters (panels a and c), and as 0.01 for ‘large’ clusters (panels b and d). Data were estimated using simulation (50,000 replications per scenario)