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. 2020 Mar 6;10:4223. doi: 10.1038/s41598-020-61046-7

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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 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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Age trend in cumulative incidence with randomized vs fixed p for the population in the CIS case; giving a distribution to p does not reduce the saturation of incidence from 100%, but slows the transition to 100%. In the randomized case, p values were drawn from a uniform distribution with range [3.775 ∗ 10⁻¹¹, 3.06 ∗ 10⁻⁷], while for the fixed case, p = 3.06 * 10⁻⁷; for both, n = 1.785 * 10⁸ and k = 5.