{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T22:15:45Z","timestamp":1792793745401,"version":"4.5.0"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T00:00:00Z","timestamp":1600992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Sanofi Pasteur and the National Institute of Allergy and Infectious Diseases","id":[{"id":"https:\/\/ror.org\/043z4tv69","id-type":"ROR","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000016","name":"Department of Health and Human Services","doi-asserted-by":"publisher","award":["R37AI054165"],"award-info":[{"award-number":["R37AI054165"]}],"id":[{"id":"10.13039\/100000016","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"NIH","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,4,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In vaccine studies, an important research question is to study effect modification of clinical treatment efficacy by intermediate biomarker-based principal strata. In settings where participants entering a trial may have prior exposure and therefore variable baseline biomarker values, clinical treatment efficacy may further depend jointly on a biomarker measured at baseline and measured at a fixed time after vaccination. This makes it important to conduct a bivariate effect modification analysis by both the intermediate biomarker-based principal strata and the baseline biomarker values. Existing research allows this assessment if the sampling of baseline and intermediate biomarkers follows a monotone pattern, i.e., if participants who have the biomarker measured post-randomization would also have the biomarker measured at baseline. However, additional complications in study design could happen in practice. For example, in a dengue correlates study, baseline biomarker values were only available from a fraction of participants who have biomarkers measured post-randomization. How to conduct the bivariate effect modification analysis in these studies remains an open research question. In this article, we propose approaches for bivariate effect modification analysis in the complicated sampling design based on an estimated likelihood framework. We demonstrate advantages of the proposed method over existing methods through numerical studies and illustrate our method with data sets from two phase 3 dengue vaccine efficacy trials.<\/jats:p>","DOI":"10.1093\/biostatistics\/kxaa040","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T07:10:25Z","timestamp":1598944225000},"page":"541-557","source":"Crossref","is-referenced-by-count":2,"title":["Evaluation of treatment effect modification by biomarkers measured pre- and post-randomization in the presence of non-monotone missingness"],"prefix":"10.1093","volume":"23","author":[{"given":"Yingying","family":"Zhuang","sequence":"first","affiliation":[{"name":"Department of Biostatistics, University of Washington , Seattle, WA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington , Seattle, WA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter B","family":"Gilbert","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington , Seattle, WA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,25]]},"reference":[{"key":"2022062217113421300_B1","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1016\/S0140-6736(14)61060-6","article-title":"Clinical efficacy and safety of a novel tetravalent dengue vaccine in healthy children in Asia: a phase 3, randomised, observer-masked, placebo-controlled trial","volume":"384","author":"Capeding,","year":"2014","journal-title":"The Lancet"},{"key":"2022062217113421300_B2","first-page":"917","article-title":"Discovering treatment effect heterogeneity through post-treatment variables with application to the effect of class size on mathematics scores","volume":"67","author":"Ertefaie,","year":"2018","journal-title":"Journal of the Royal Statistical Society: Series C (Applied Statistics)"},{"key":"2022062217113421300_B3","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1111\/j.1541-0420.2006.00569.x","article-title":"Augmented designs to assess immune response in vaccine trials","volume":"62","author":"Follmann,","year":"2006","journal-title":"Biometrics"},{"key":"2022062217113421300_B4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1111\/j.0006-341X.2002.00021.x","article-title":"Principal stratification in causal inference","volume":"58","author":"Frangakis,","year":"2002","journal-title":"Biometrics"},{"key":"2022062217113421300_B5","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1080\/01621459.2011.643719","article-title":"Evaluating the effect of training on wages in the presence of noncompliance, nonemployment, and missing outcome data","volume":"107","author":"Frumento,","year":"2012","journal-title":"Journal of the American Statistical Association"},{"key":"2022062217113421300_B6","doi-asserted-by":"crossref","first-page":"164","DOI":"10.4269\/ajtmh.18-0534","article-title":"Bridging efficacy of a tetravalent dengue vaccine from children\/adolescents to adults in highly endemic countries based on neutralizing antibody response","volume":"101","author":"Gilbert,","year":"2019","journal-title":"The American Journal of Tropical Medicine and Hygiene"},{"key":"2022062217113421300_B7","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1111\/j.1541-0420.2008.01014.x","article-title":"Evaluating candidate principal surrogate endpoints","volume":"64","author":"Gilbert,","year":"2008","journal-title":"Biometrics"},{"key":"2022062217113421300_B8","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/biom.12014","article-title":"Design and estimation for evaluating principal surrogate markers in vaccine trials","volume":"69","author":"Huang,","year":"2013","journal-title":"Biometrics"},{"key":"2022062217113421300_B9","first-page":"1","article-title":"On the application of probability theory to agricultural experiments. essay on principles. 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