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. 2022 Apr 22;12:6627. doi: 10.1038/s41598-022-09069-0

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© The Author(s) 2022

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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Comparison of estimation biases by meta-analysis and ODACH in the opioid use disorder study. Presented are the estimated log hazard ratios (HRs) with 95% confidence intervals for risk factors for opioid use disorder using pooled analysis (blue), meta-analysis (green), and One-shot Distributed Algorithm for multicenter Cox proportional hazards model with heterogeneous hazard (ODACH) (red). The analyses used data of N = 14,015 patients from five clinical sites in the OneFlorida Clinical Research Consortium.