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In this design setting, a unit of randomization can be assigned to any combination of interventions. The rationale for taking this kind of approach can vary depending on the specific questions targeted by the research. These questions, in turn, have implications for the way in which the analyses will be conducted. The goal in this paper is to describe how we developed a factorial design along with a Bayesian analytic plan for a large cluster\u2010randomized trial\u2014the\n                    <jats:italic>Emergency Departments LEading the transformation of Alzheimer's and Dementia care<\/jats:italic>\n                    (ED\u2010LEAD) study\u2014focused on improving care for persons living with dementia.\n                  <\/jats:p>","DOI":"10.1002\/sim.70264","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:40:56Z","timestamp":1757313656000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Bayesian Multi\u2010Factorial Design and Analysis for Estimating Combined Effects of Multiple Interventions in a Pragmatic Clinical Trial to Improve Dementia Care"],"prefix":"10.1002","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0292-8780","authenticated-orcid":false,"given":"Keith S.","family":"Goldfeld","sequence":"first","affiliation":[{"name":"Division of Biostatistics, Department of Population Health New York University Grossman School of Medicine  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Corita R.","family":"Grudzen","sequence":"additional","affiliation":[{"name":"Department of Medicine Memorial Sloan Kettering Cancer Center  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manish N.","family":"Shah","sequence":"additional","affiliation":[{"name":"BerbeeWalsh Department of Emergency Medicine University of Wisconsin School of Medicine and Public Health  Madison Wisconsin USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3405-7043","authenticated-orcid":false,"given":"Abraham A.","family":"Brody","sequence":"additional","affiliation":[{"name":"Rory Meyers College of Nursing New York University  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joshua","family":"Chodosh","sequence":"additional","affiliation":[{"name":"Division of Geriatric Medicine and Palliative Care, Department of Medicine New York University Grossman School of Medicine  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-7792","authenticated-orcid":false,"given":"Rebecca","family":"Anthopolos","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, Department of Population Health New York University Grossman School of Medicine  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,9,7]]},"reference":[{"key":"e_1_2_12_2_1","volume-title":"The Design of Experiments","author":"Fisher R. 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