{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T13:02:11Z","timestamp":1781701331544,"version":"3.54.5"},"reference-count":34,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T00:00:00Z","timestamp":1774569600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"NIH","award":["R01CA269696"],"award-info":[{"award-number":["R01CA269696"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>Covariate-specific and time-dependent area-under-curve (AUC) is often used to evaluate the discriminative performance of biomarkers with time-to-event outcomes, particularly when certain covariates influence biomarkers\u2019 accuracy. In biomarker research, despite extensive efforts, missing data remain unavoidable, with nonignorable missingness posing significant challenges. This article focuses on estimating the impact of covariates on time-dependent AUC in the presence of nonignorable missing biomarkers. Assuming a parametric model on the missing probability, we leverage instrumental variables to address the\u00a0identifiable issue and estimate the unknown parameters. We integrate the inverse probability weighting approach into the score equation of a pseudo partial likelihood for estimation and inference. Additionally, we establish the asymptotic properties of the proposed estimators. Through simulation studies, we evaluate finite sample performance of the proposed estimators, and apply the method to data from the Alzheimer\u2019s Disease Neuroimaging Initiative (ADNI) database.<\/jats:p>","DOI":"10.1177\/09622802261432996","type":"journal-article","created":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T14:46:05Z","timestamp":1774622765000},"page":"1078-1090","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Addressing nonignorable missing data and heterogeneity in prognostic biomarker assessment"],"prefix":"10.1177","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8126-9735","authenticated-orcid":false,"given":"Xinran","family":"Huang","sequence":"first","affiliation":[{"name":"The University of Texas Health Science Center at Houston"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3595-4392","authenticated-orcid":false,"given":"Ruosha","family":"Li","sequence":"additional","affiliation":[{"name":"The University of Texas Health Science Center at Houston"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5289-331X","authenticated-orcid":false,"given":"Jing","family":"Ning","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, The University of Texas MD Anderson Cancer Center, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"for the Alzheimer\u2019s Disease Neuroimaging Initiative","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,3,27]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejca.2008.03.006"},{"key":"e_1_3_3_3_2","unstructured":"FDA-NIHBiomarker Working Group. Prognostic biomarker. In BEST (biomarkers endpointS and other tools) resource [Internet]. Silver Spring MD: Food and Drug Administration (US) 2016."},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2005.030814.x"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1093\/jnci\/93.14.1054"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214503000198"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/kwn099"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.10046"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.10024"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1177\/09622802241262521"},{"key":"e_1_3_3_11_2","first-page":"606802","article-title":"CSF biomarkers for Alzheimer\u2019s disease diagnosis","volume":"2010","author":"Anoop A","year":"2010","unstructured":"Anoop A, Singh PK, Jacob RS et al. CSF biomarkers for Alzheimer\u2019s disease diagnosis. Int J Alzheimers Dis 2010; 2010: 606802.","journal-title":"Int J Alzheimers Dis"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0173(00)00019-9"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1385\/MN:24:1-3:087"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1001\/jama.289.16.2094"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","unstructured":"Little RJA Rubin DB. Theory of inference based on the likelihood function. In Statistical analysis with missing data. John Wiley & Sons Ltd. 2002 pp.95\u2013132. DOI: 10.1002\/9781119013563.ch6.","DOI":"10.1002\/9781119013563.ch6"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2011.tm10104"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10473840"},{"key":"e_1_3_3_18_2","first-page":"1097","article-title":"An instrumental variable approach for identification and estimation with nonignorable nonresponse","volume":"24","author":"Wang S","year":"2014","unstructured":"Wang S, Shao J, Kim JK. An instrumental variable approach for identification and estimation with nonignorable nonresponse. Stat Sin 2014; 24: 1097\u20131116.","journal-title":"Stat Sin"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.1093\/jssam\/smv047"},{"key":"e_1_3_3_20_2","volume-title":"Semiparametric theory and missing data","author":"Tsiatis AA","year":"2006","unstructured":"Tsiatis AA. Semiparametric theory and missing data. New York, NY: Springer, 2006."},{"key":"e_1_3_3_21_2","first-page":"723","article-title":"Empirical likelihood for estimating equations in nonignorable missing data","volume":"24","author":"Tang N","year":"2014","unstructured":"Tang N, Zhao P, Zhu H. Empirical likelihood for estimating equations in nonignorable missing data. Stat Sin 2014; 24: 723\u2013747.","journal-title":"Stat Sin"},{"key":"e_1_3_3_22_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.983234"},{"key":"e_1_3_3_23_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12312"},{"key":"e_1_3_3_24_2","doi-asserted-by":"publisher","DOI":"10.1080\/10543406.2023.2170394"},{"key":"e_1_3_3_25_2","doi-asserted-by":"publisher","unstructured":"Little RJA Rubin DB. Nonignorable missing-data models chapter 15. John Wiley & Sons Ltd 2002. pp.312\u2013348. DOI: 10.1002\/9781119013563.ch15.","DOI":"10.1002\/9781119013563.ch15"},{"key":"e_1_3_3_26_2","first-page":"817","article-title":"Regression analysis for the partial area under the ROC curve","volume":"18","author":"Cai T","year":"2008","unstructured":"Cai T, Dodd LE. Regression analysis for the partial area under the ROC curve. Stat Sin 2008; 18: 817\u2013836.","journal-title":"Stat Sin"},{"key":"e_1_3_3_27_2","doi-asserted-by":"publisher","unstructured":"Newey WK McFadden D. Chapter 36 Large sample estimation and hypothesis testing. In Handbook of econometrics. Vol. 4. Elsevier 1994. pp.2111\u20132245. DOI: 10.1016\/S1573-4412(05)80005-4.","DOI":"10.1016\/S1573-4412(05)80005-4"},{"key":"e_1_3_3_28_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1801447"},{"key":"e_1_3_3_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-018-9451-6"},{"key":"e_1_3_3_30_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12761"},{"key":"e_1_3_3_31_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13024-022-00574-4"},{"key":"e_1_3_3_32_2","doi-asserted-by":"publisher","DOI":"10.1002\/alz.054422"},{"key":"e_1_3_3_33_2","article-title":"Longitudinal CSF Alzheimer\u2019s disease biomarker changes from middle age to late adulthood","volume":"14","author":"Pettigrew C","year":"2022","unstructured":"Pettigrew C, Soldan A, Wang J et al. Longitudinal CSF Alzheimer\u2019s disease biomarker changes from middle age to late adulthood. Alzheimers Dement (Amst) 2022; 14: e12374.","journal-title":"Alzheimers Dement (Amst)"},{"key":"e_1_3_3_34_2","doi-asserted-by":"publisher","DOI":"10.1080\/03610921003764282"},{"key":"e_1_3_3_35_2","doi-asserted-by":"publisher","DOI":"10.1177\/0962280215584401"}],"container-title":["Statistical Methods in Medical Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09622802261432996","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/09622802261432996","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09622802261432996","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T12:21:34Z","timestamp":1781698894000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/09622802261432996"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,27]]},"references-count":34,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["10.1177\/09622802261432996"],"URL":"https:\/\/doi.org\/10.1177\/09622802261432996","relation":{},"ISSN":["0962-2802","1477-0334"],"issn-type":[{"value":"0962-2802","type":"print"},{"value":"1477-0334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,27]]}}}