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The regression coefficients of the ZIP model have latent class interpretations, which correspond to a susceptible subpopulation at risk for the condition with counts generated from a Poisson distribution and a non\u2010susceptible subpopulation that provides the extra or excess zeros. The ZIP model parameters, however, are not well suited for inference targeted at marginal means, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. We develop a marginalized ZIP model approach for independent responses to model the population mean count directly, allowing straightforward inference for overall exposure effects and empirical robust variance estimation for overall log\u2010incidence density ratios. Through simulation studies, the performance of maximum likelihood estimation of the marginalized ZIP model is assessed and compared with other methods of estimating overall exposure effects. The marginalized ZIP model is applied to a recent study of a motivational interviewing\u2010based safer sex counseling intervention, designed to reduce unprotected sexual act counts. Copyright \u00a9 2014 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.6293","type":"journal-article","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T03:32:59Z","timestamp":1410751979000},"page":"5151-5165","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":90,"title":["A marginalized zero\u2010inflated Poisson regression model with overall exposure effects"],"prefix":"10.1002","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8614-7190","authenticated-orcid":false,"given":"D. Leann","family":"Long","sequence":"first","affiliation":[{"name":"Department of Biostatistics West Virginia University  Morgantown WV U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John S.","family":"Preisser","sequence":"additional","affiliation":[{"name":"Department of Biostatistics University of North Carolina at Chapel Hill  Chapel Hill NC U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amy H.","family":"Herring","sequence":"additional","affiliation":[{"name":"Department of Biostatistics University of North Carolina at Chapel Hill  Chapel Hill NC U.S.A."},{"name":"Carolina Population Center University of North Carolina at Chapel Hill  Chapel Hill NC U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carol E.","family":"Golin","sequence":"additional","affiliation":[{"name":"Department of Health Behavior University of North Carolina at Chapel Hill  Chapel Hill NC U.S.A."},{"name":"Department of Medicine University of North Carolina at Chapel Hill  Chapel Hill NC U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2014,9,14]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-985X.00130"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90002-3"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/1269547"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280211407800"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1159\/000338992"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.1999.00688.x"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2010.07.005"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2011.11.021"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1089\/apc.2009.0252"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.4710360505"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0013"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912526"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10461-011-0025-9"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.6293","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.6293","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.6293","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T03:52:39Z","timestamp":1694663559000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.6293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,14]]},"references-count":13,"journal-issue":{"issue":"29","published-print":{"date-parts":[[2014,12,20]]}},"alternative-id":["10.1002\/sim.6293"],"URL":"https:\/\/doi.org\/10.1002\/sim.6293","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,14]]}}}