{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T01:16:53Z","timestamp":1785201413347,"version":"3.55.0"},"reference-count":32,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000060","name":"National Institute of Allergy and Infectious Diseases","doi-asserted-by":"publisher","award":["R01 AI136947"],"award-info":[{"award-number":["R01 AI136947"]}],"id":[{"id":"10.13039\/100000060","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000060","name":"National Institute of Allergy and Infectious Diseases","doi-asserted-by":"publisher","award":["T32 AI007358"],"award-info":[{"award-number":["T32 AI007358"]}],"id":[{"id":"10.13039\/100000060","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2024,3,30]]},"abstract":"<jats:p>Generalized estimating equations (GEEs) provide a useful framework for estimating marginal regression parameters based on data from cluster randomized trials (CRTs), but they can result in inaccurate parameter estimates when some outcomes are informatively missing. Existing techniques to handle missing outcomes in CRTs rely on correct specification of a propensity score model, a covariate\u2010conditional mean outcome model, or require at least one of these two models to be correct, which can be challenging in practice. In this article, we develop new weighted GEEs to simultaneously estimate the marginal mean, scale, and correlation parameters in CRTs with missing outcomes, allowing for multiple propensity score models and multiple covariate\u2010conditional mean models to be specified. The resulting estimators are consistent provided that any one of these models is correct. An iterative algorithm is provided for implementing this more robust estimator and practical considerations for specifying multiple models are discussed. We evaluate the performance of the proposed method through Monte Carlo simulations and apply the proposed multiply robust estimator to analyze the Botswana Combination Prevention Project, a large HIV prevention CRT designed to evaluate whether a combination of HIV\u2010prevention measures can reduce HIV incidence.<\/jats:p>","DOI":"10.1002\/sim.10027","type":"journal-article","created":{"date-parts":[[2024,2,7]],"date-time":"2024-02-07T05:56:36Z","timestamp":1707285396000},"page":"1458-1474","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multiply robust generalized estimating equations for cluster randomized trials with missing outcomes"],"prefix":"10.1002","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3829-7079","authenticated-orcid":false,"given":"Dustin J.","family":"Rabideau","sequence":"first","affiliation":[{"name":"Biostatistics Massachusetts General Hospital  Boston Massachusetts USA"},{"name":"Department of Medicine Harvard Medical School  Boston Massachusetts USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-1893","authenticated-orcid":false,"given":"Fan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Yale University School of Public Health  New Haven Connecticut USA"},{"name":"Center for Methods in Implementation and Prevention Science Yale University  New Haven Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5007-193X","authenticated-orcid":false,"given":"Rui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Population Medicine Harvard Pilgrim Health Care Institute and Harvard Medical School  Boston Massachusetts USA"},{"name":"Department of Biostatistics Harvard T. 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