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This is particularly relevant when performing mediation analysis (possibly in a causal framework) with stratified case\u2013control (SCC) data in settings where both the outcome and the mediator are binary. Despite being designed for parametric identification, our strategy is general and can be used also in a nonparametric context. With reference to parametric estimation, we derive the maximum likelihood (ML) estimator and the M\u2010estimator of the joint outcome\u2013mediator parameter vector. We then conduct a simulation study focusing on the main causal mediation quantities (i.e., natural effects) and comparing M\u2010 and ML estimation to existing methods, based on weighting. As an illustrative example, we reanalyze a German CC data set in order to investigate whether the effect of reduced immunocompetency on listeriosis onset is mediated by the intake of gastric acid\u00a0suppressors.<\/jats:p>","DOI":"10.1002\/bimj.202300089","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T23:07:02Z","timestamp":1705100822000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mediation analysis with case\u2013control sampling: Identification and estimation in the presence of a binary mediator"],"prefix":"10.1002","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1050-4742","authenticated-orcid":false,"given":"Marco","family":"Doretti","sequence":"first","affiliation":[{"name":"Department of Statistics, Computer Science, and Applications University of Florence Florence Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minna","family":"Genb\u00e4ck","sequence":"additional","affiliation":[{"name":"Department of Statistics, USBE Ume\u00e5 University Ume\u00e5 Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elena","family":"Stanghellini","sequence":"additional","affiliation":[{"name":"Department of Statistics, USBE Ume\u00e5 University Ume\u00e5 Sweden"},{"name":"Department of Economics University of Perugia Perugia Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,1,12]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1742-1241.2012.02973.x"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201400124"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/59.1.19"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1097\/EDE.0000000000001313"},{"key":"e_1_2_11_6_1","unstructured":"Avin C. 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