{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T07:13:58Z","timestamp":1791357238066,"version":"4.3.1"},"reference-count":30,"publisher":"Wiley","issue":"27","license":[{"start":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T00:00:00Z","timestamp":1251936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T00:00:00Z","timestamp":1251936000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T00:00:00Z","timestamp":1251936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000027","name":"NIAAA","doi-asserted-by":"crossref","award":["1 R21 AA10948-01A1"],"award-info":[{"award-number":["1 R21 AA10948-01A1"]}],"id":[{"id":"10.13039\/100000027","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000025","name":"NIMH","doi-asserted-by":"crossref","award":["MH40859"],"award-info":[{"award-number":["MH40859"]}],"id":[{"id":"10.13039\/100000025","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NIDA","award":["P30 MH066247"],"award-info":[{"award-number":["P30 MH066247"]}]}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2009,11,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Placebo\u2010controlled randomized trials for antidepressants and other drugs often show a response for a sizeable percentage of the subjects in the placebo group. Potential placebo responders can be assumed to exist also in the drug treatment group, making it difficult to assess the drug effect. A key drug research focus should be to estimate the percentage of individuals among those who responded to the drug who would not have responded to the placebo (\u2018Drug Only Responders\u2019). This paper investigates a finite mixture model approach to uncover percentages of up to four potential mixture components: Never Responders, Drug Only Responders, Placebo Only Responders, and Always Responders. Two examples are used to illustrate the modeling, a 12\u2010week antidepressant trial with a continuous outcome (Hamilton D score) and a 7\u2010week schizophrenia trial with a binary outcome (illness level). The approach is formulated in causal modeling terms using potential outcomes and principal stratification. Growth mixture modeling (GMM) with maximum\u2010likelihood estimation is used to uncover the different mixture components. The results point to the limitations of the conventional approach of comparing marginal response rates for drug and placebo groups. It is useful to augment such reporting with the GMM\u2010estimated prevalences for the four classes of subjects and the Drug Only Responder drug effect estimate. Copyright \u00a9 2009 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.3721","type":"journal-article","created":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T14:30:30Z","timestamp":1251988230000},"page":"3363-3385","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Estimating drug effects in the presence of placebo response: Causal inference using growth mixture modeling"],"prefix":"10.1002","volume":"28","author":[{"given":"Bengt","family":"Muth\u00e9n","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hendricks C.","family":"Brown","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2009,9,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1176\/appi.ajp.157.3.344"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0924-977X(94)90093-0"},{"key":"e_1_2_1_4_2","volume-title":"Longitudinal Data Analysis","author":"Hedeker D","year":"2006"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476902"},{"key":"e_1_2_1_6_2","first-page":"449","volume-title":"Sociological Methodology","author":"Holland P","year":"1988"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344064"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2002.00021.x"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.3.2.147"},{"key":"e_1_2_1_11_2","first-page":"438","article-title":"Random regression models: a comprehensive approach to the analysis of longitudinal psychiatric data","volume":"24","author":"Gibbons RD","year":"1988","journal-title":"Psychopharmacology Bulletin"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1001\/archpsyc.1984.01790190056007"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/3.4.459"},{"key":"e_1_2_1_14_2","first-page":"143","volume-title":"Longitudinal Data Analysis","author":"Muth\u00e9n B","year":"2008"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2004.02-123.x"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/5.2.207"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3533"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471721182"},{"key":"e_1_2_1_19_2","volume-title":"Statistical Analysis of Finite Mixture Distributions","author":"Titterington DM","year":"1985"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.1999.00463.x"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214502753479220"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxh022"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2007.00837.x"},{"key":"e_1_2_1_24_2","volume-title":"Mplus User's Guide","author":"Muth\u00e9n B","year":"2008"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344136"},{"key":"e_1_2_1_26_2","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/01621459.1995.10476572","article-title":"Bayes factors","volume":"90","author":"Kass RE","year":"1993","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.1080\/10705510701575396"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1287\/mksc.12.1.103"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214503000000783"},{"key":"e_1_2_1_30_2","doi-asserted-by":"publisher","DOI":"10.2202\/1557\u20104679.1152"},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.1081\/BIP-120008848"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3721","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3721","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.3721","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T10:11:29Z","timestamp":1699956689000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.3721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,3]]},"references-count":30,"journal-issue":{"issue":"27","published-print":{"date-parts":[[2009,11,30]]}},"alternative-id":["10.1002\/sim.3721"],"URL":"https:\/\/doi.org\/10.1002\/sim.3721","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,3]]}}}