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Background Implementation of multifaceted interventions typically involves many diverse elements working together in interrelated ways, including intervention components, implementation strategies, and features of local context. Given this real-world complexity, implementation researchers may be interested in a new mathematical, cross-case method called Coincidence Analysis (CNA) that has been designed explicitly to support causal inference, answer research questions about combinations of conditions that are minimally necessary or sufficient for an outcome, and identify the possible presence of multiple causal paths to an outcome. CNA can be applied as a standalone method or in conjunction with other approaches and can reveal new empirical findings related to implementation that might otherwise have gone undetected. Methods We applied CNA to a publicly available dataset from Sweden with county-level data on human papillomavirus (HPV) vaccination campaigns and vaccination uptake in 2012 and 2014 and then compared CNA results to the published regression findings. Results The original regression analysis found vaccination uptake was positively associated only with the availability of vaccines in schools. CNA produced different findings and uncovered an additional solution path: high vaccination rates were achieved by either (1) offering the vaccine in all schools or (2) a combination of offering the vaccine in some schools and media coverage. Conclusions CNA offers a new comparative approach for researchers seeking to understand how implementation conditions work together and link to outcomes.

Department of Implementation Science, Wake Forest School of Medicine, 525@Vine Room 5219, Medical Center Boulevard, Winston-Salem, NC, 27157, USA Sarah Birken Authors 1. Rights and permissions 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. Coincidence analysis: a new method for causal inference in implementation science [RAW_REF_TEXT] Rebecca Garr Whitaker1 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Nina Sperber2 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Michael Baumgartner3 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Alrik Thiem4 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Deborah Cragun5 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Laura Damschroder6 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Edward J. Miech7 , [/RAW_REF_TEXT] [RAW_REF_TEXT] Alecia Slade8 & [/RAW_REF_TEXT] [RAW_REF_TEXT] Sarah Birken 9 [/RAW_REF_TEXT] Implementation Science volume 16, Article number: 11 (2021) Cite this article [RAW_REF_TEXT] 117 Accesses [/RAW_REF_TEXT] [RAW_REF_TEXT] 1 Altmetric [/RAW_REF_TEXT] [RAW_REF_TEXT] Metrics details [/RAW_REF_TEXT] [RAW_REF_TEXT] The original article was published in Implementation Science 2020 15:108 [/RAW_REF_TEXT] Correction to: Coincidence analysis: a new method for causal inference in implementation science [RAW_REF_TEXT] Rebecca Garr Whitaker1 , Nina Sperber2 , Michael Baumgartner3 , Alrik Thiem4 , Deborah Cragun5 , Laura Damschroder6 , Edward J. Miech7 , Alecia Slade8 & Sarah Birken 9 [/RAW_REF_TEXT] Implementation Science volume 16, Article number: 11 (2021) Cite this article [RAW_REF_TEXT] 117 Accesses 1 Altmetric Metrics details The original article was published in Implementation Science 2020 15:108

Background: Implementation of multifaceted interventions typically involves many diverse elements working together in interrelated ways, including intervention components, implementation strategies, and features of local context. Given this real-world complexity, implementation researchers may be interested in a new mathematical, cross-case method called Coincidence Analysis (CNA) that has been designed explicitly to support causal inference, answer research questions about combinations of conditions that are minimally necessary or sufficient for an outcome, and identify the possible presence of multiple causal paths to an outcome. CNA can be applied as a standalone method or in conjunction with other approaches, and can reveal new empirical findings related to implementation that might otherwise have gone undetected. Methods: We applied CNA to a publicly available dataset from Sweden with county-level data on human papillomavirus (HPV) vaccination campaigns and vaccination uptake in 2012 and 2014 and then compared CNA results to the published regression findings. Results: The original regression analysis found vaccination uptake was positively associated only with the availability of vaccines in schools. CNA produced different findings and uncovered an additional solution path: high vaccination rates were achieved by either (1) offering the vaccine in all schools or (2) a combination of offering the vaccine in some schools and media coverage. Conclusions. CNA offers a new comparative approach for researchers seeking to understand how implementation conditions work together and link to outcomes.