{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:03:26Z","timestamp":1792785806394,"version":"4.5.0"},"reference-count":50,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"United States National Institutes of Health","award":["R01-GM133848"],"award-info":[{"award-number":["R01-GM133848"]}],"id":[{"id":"https:\/\/ror.org\/01cwqze88","id-type":"ROR","asserted-by":"crossref"}]},{"name":"United States National Institutes of Health","award":["RF1-AG090462"],"award-info":[{"award-number":["RF1-AG090462"]}],"id":[{"id":"https:\/\/ror.org\/01cwqze88","id-type":"ROR","asserted-by":"crossref"}]},{"name":"United States National Institutes of Health","award":["R01-HL141989"],"award-info":[{"award-number":["R01-HL141989"]}],"id":[{"id":"https:\/\/ror.org\/01cwqze88","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,20]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Regression analysis of correlated data, where multiple correlated responses are recorded on the same unit, is ubiquitous in many scientific areas. With the advent of new technologies, in particular high-throughput omics profiling assays, such correlated data increasingly consist of a large number of variables compared with the available sample size. Motivated by recent longitudinal proteomics studies of COVID-19, we propose a novel inference procedure for linear functionals of high-dimensional regression coefficients in generalized estimating equations, which are widely used to analyze correlated data. Our estimator for this more general inferential target, obtained via constructing projected estimating equations, is shown to be asymptotically normally distributed under mild regularity conditions. We also introduce a data-driven cross-validation procedure to select the tuning parameter for estimating the projection direction, which is not addressed in the existing procedures. We illustrate the utility of the proposed procedure in providing confidence intervals for associations of individual proteins and severe COVID risk scores obtained based on high-dimensional proteomics data, and demonstrate its robust finite-sample performance, especially in estimation bias and confidence interval coverage, via extensive simulations.<\/jats:p>","DOI":"10.1093\/biostatistics\/kxag013","type":"journal-article","created":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T11:12:04Z","timestamp":1776510724000},"source":"Crossref","is-referenced-by-count":2,"title":["Statistical inference for high-dimensional generalized estimating equations"],"prefix":"10.1093","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1561-6871","authenticated-orcid":false,"given":"Lu","family":"Xia","sequence":"first","affiliation":[{"name":"Department of Statistics and Probability, Michigan State University , 619 Red Cedar Road , East Lansing, MI, 48824,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8846-3533","authenticated-orcid":false,"given":"Ali","family":"Shojaie","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Department of Statistics, University of Washington , 3980 15th Avenue NE , Seattle, WA, 98105,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"2026102110244910400_kxag013-B1","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1214\/009053604000001255","article-title":"Asymptotic results with generalized estimating equations for longitudinal data","volume":"33","author":"Balan","year":"2005","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B2","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini","year":"1995","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"key":"2026102110244910400_kxag013-B3","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1214\/aos\/1013699998","article-title":"The control of the false discovery rate in multiple testing under dependency","volume":"29","author":"Benjamini","year":"2001","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B4","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1080\/01621459.2019.1660172","article-title":"Fixed effects testing in high-dimensional linear mixed models","volume":"115","author":"Bradic","year":"2020","journal-title":"J Am Stat Assoc"},{"key":"2026102110244910400_kxag013-B5","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.3150\/12-BEJSP11","article-title":"Statistical significance in high-dimensional linear models","volume":"19","author":"B\u00fchlmann","year":"2013","journal-title":"Bernoulli"},{"key":"2026102110244910400_kxag013-B6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1146\/annurev-statistics-022513-115545","article-title":"High-dimensional statistics with a view toward applications in biology","volume":"1","author":"B\u00fchlmann","year":"2014","journal-title":"Ann Rev Stat Appl"},{"key":"2026102110244910400_kxag013-B7","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1016\/j.jspi.2013.05.019","article-title":"Correlated variables in regression: clustering and sparse estimation","volume":"143","author":"B\u00fchlmann","year":"2013","journal-title":"J Stat Plan Inference"},{"key":"2026102110244910400_kxag013-B8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-20192-9","volume-title":"Statistics for High-Dimensional data: Methods, Theory and Applications","author":"B\u00fchlmann","year":"2011"},{"key":"2026102110244910400_kxag013-B9","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1198\/jasa.2011.tm10155","article-title":"A constrained $ \\ell_{1} $ minimization approach to sparse precision matrix estimation","volume":"106","author":"Cai","year":"2011","journal-title":"J Am Stat Assoc"},{"key":"2026102110244910400_kxag013-B10","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1142\/9789812837448_0003","volume-title":"Frontiers of Statistics, volume 1: New Developments in Biostatistics and Bioinformatics.","author":"Dziak","year":"2009"},{"key":"2026102110244910400_kxag013-B11","doi-asserted-by":"crossref","first-page":"104552","DOI":"10.1016\/j.ebiom.2023.104552","article-title":"Cellular and molecular biomarkers of long COVID: a scoping review","volume":"91","author":"Esp\u00edn","year":"2023","journal-title":"EBioMedicine"},{"key":"2026102110244910400_kxag013-B12","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1214\/12-AOS1028","article-title":"Variable selection in linear mixed effects models","volume":"40","author":"Fan","year":"2012","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B13","doi-asserted-by":"crossref","first-page":"2622","DOI":"10.1214\/19-AOS1900","article-title":"Test of significance for high-dimensional longitudinal data","volume":"48","author":"Fang","year":"2020","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B14","doi-asserted-by":"crossref","first-page":"100680","DOI":"10.1016\/j.xcrm.2022.100680","article-title":"Integrated plasma proteomic and single-cell immune signaling network signatures demarcate mild, moderate, and severe COVID-19","volume":"3","author":"Feyaerts","year":"2022","journal-title":"Cell Rep Med"},{"key":"2026102110244910400_kxag013-B15","doi-asserted-by":"crossref","first-page":"100287","DOI":"10.1016\/j.xcrm.2021.100287","article-title":"Longitudinal proteomic analysis of severe COVID-19 reveals survival-associated signatures, tissue-specific cell death, and cell-cell interactions","volume":"2","author":"Filbin","year":"2021","journal-title":"Cell Rep Med"},{"key":"2026102110244910400_kxag013-B16","volume-title":"Applied longitudinal analysis","author":"Fitzmaurice","year":"2012"},{"key":"2026102110244910400_kxag013-B17","volume-title":"Data analysis using regression and multilevel\/hierarchical models","author":"Gelman","year":"2007"},{"key":"2026102110244910400_kxag013-B18","doi-asserted-by":"crossref","first-page":"20533","DOI":"10.1038\/s41598-020-77525-w","article-title":"Longitudinal proteomic profiling reveals increased early inflammation and sustained apoptosis proteins in severe COVID-19","volume":"10","author":"Haljasm\u00e4gi","year":"2020","journal-title":"Sci Rep"},{"key":"2026102110244910400_kxag013-B19","first-page":"2869","article-title":"Confidence intervals and hypothesis testing for high-dimensional regression","volume":"15","author":"Javanmard","year":"2014","journal-title":"J Mach Learn Res"},{"key":"2026102110244910400_kxag013-B20","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.cytogfr.2020.06.008","article-title":"IL-15 immunotherapy is a viable strategy for COVID-19","volume":"54","author":"Kandikattu","year":"2020","journal-title":"Cytokine Growth Factor Rev"},{"key":"2026102110244910400_kxag013-B21","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1080\/01621459.2021.1888740","article-title":"Inference for high-dimensional linear mixed-effects models: a quasi-likelihood approach","volume":"117","author":"Li","year":"2022","journal-title":"J Am Stat Assoc"},{"key":"2026102110244910400_kxag013-B22","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","article-title":"Longitudinal data analysis using generalized linear models","volume":"73","author":"Liang","year":"1986","journal-title":"Biometrika"},{"key":"2026102110244910400_kxag013-B23","first-page":"171","author":"Lin","year":"2020"},{"key":"2026102110244910400_kxag013-B24","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1080\/01621459.2019.1699421","article-title":"Global and simultaneous hypothesis testing for high-dimensional logistic regression models","volume":"116","author":"Ma","year":"2021","journal-title":"J Am Stat Assoc"},{"key":"2026102110244910400_kxag013-B25","doi-asserted-by":"crossref","DOI":"10.1002\/9780470510445","volume-title":"Missing data in clinical studies","author":"Molenberghs","year":"2007"},{"key":"2026102110244910400_kxag013-B26","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1214\/18-STS661","article-title":"A unified theory of confidence regions and testing for high-dimensional estimating equations","volume":"33","author":"Neykov","year":"2018","journal-title":"Statist Sci"},{"key":"2026102110244910400_kxag013-B27","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1214\/16-AOS1448","article-title":"A general theory of hypothesis tests and confidence regions for sparse high dimensional models","volume":"45","author":"Ning","year":"2017","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B28","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1111\/j.0006-341X.2001.00120.x","article-title":"Akaike\u2019s information criterion in generalized estimating equations","volume":"57","author":"Pan","year":"2001","journal-title":"Biometrics"},{"key":"2026102110244910400_kxag013-B29","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1002\/sim.1241","article-title":"Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random","volume":"21","author":"Preisser","year":"2002","journal-title":"Stat Med"},{"key":"2026102110244910400_kxag013-B30","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1093\/biomet\/87.4.823","article-title":"Improving generalised estimating equations using quadratic inference functions","volume":"87","author":"Qu","year":"2000","journal-title":"Biometrika"},{"key":"2026102110244910400_kxag013-B31","first-page":"2241","article-title":"Restricted eigenvalue properties for correlated gaussian designs","volume":"11","author":"Raskutti","year":"2010","journal-title":"J Mach Learn Res"},{"key":"2026102110244910400_kxag013-B32","doi-asserted-by":"crossref","first-page":"e1009662","DOI":"10.1371\/journal.ppat.1009662","article-title":"Signal-regulatory protein alpha is an anti-viral entry factor targeting viruses using endocytic pathways","volume":"17","author":"Sarute","year":"2021","journal-title":"PLoS Pathog"},{"key":"2026102110244910400_kxag013-B33","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.cell.2020.05.032","article-title":"Proteomic and metabolomic characterization of COVID-19 patient sera","volume":"182","author":"Shen","year":"2020","journal-title":"Cell"},{"key":"2026102110244910400_kxag013-B34","doi-asserted-by":"crossref","first-page":"9440","DOI":"10.1073\/pnas.1530509100","article-title":"Statistical significance for genomewide studies","volume":"100","author":"Storey","year":"2003","journal-title":"Proc Natl Acad Sci U S A"},{"key":"2026102110244910400_kxag013-B35","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1214\/14-AOS1221","article-title":"On asymptotically optimal confidence regions and tests for high-dimensional models","volume":"42","author":"van de","year":"2014","journal-title":"Ann Stat"},{"key":"2026102110244910400_kxag013-B36","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1214\/12-STS397","article-title":"Quasi-likelihood and\/or robust estimation in high dimensions","volume":"27","author":"van de Geer","year":"2012","journal-title":"Statist Sci"},{"key":"2026102110244910400_kxag013-B37","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1111\/j.1467-9868.2008.00679.x","article-title":"Consistent model selection and data-driven smooth tests for longitudinal data in the estimating equations approach","volume":"71","author":"Wang","year":"2009","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"key":"2026102110244910400_kxag013-B38","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1111\/j.1541-0420.2011.01678.x","article-title":"Penalized generalized estimating equations for high-dimensional longitudinal data analysis","volume":"68","author":"Wang","year":"2012","journal-title":"Biometrics"},{"key":"2026102110244910400_kxag013-B39","doi-asserted-by":"crossref","first-page":"4003","DOI":"10.1002\/sim.5479","article-title":"A bias-corrected covariance estimate for improved inference with quadratic inference functions","volume":"31","author":"Westgate","year":"2012","journal-title":"Stat Med"},{"key":"2026102110244910400_kxag013-B40","doi-asserted-by":"crossref","first-page":"2209","DOI":"10.1002\/sim.5329","article-title":"The effect of cluster size imbalance and covariates on the estimation performance of quadratic inference functions","volume":"31","author":"Westgate","year":"2012","journal-title":"Stat Med"},{"key":"2026102110244910400_kxag013-B41","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1111\/biom.13587","article-title":"Debiased lasso for generalized linear models with a diverging number of covariates","volume":"79","author":"Xia","year":"2023","journal-title":"Biometrics"},{"key":"2026102110244910400_kxag013-B42","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1111\/sjos.12595","article-title":"Statistical inference for cox proportional hazards models with a diverging number of covariates","volume":"50","author":"Xia","year":"2023","journal-title":"Scand Stat Theory Appl"},{"key":"2026102110244910400_kxag013-B43","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/s41590-023-01724-6","article-title":"Long COVID manifests with T cell dysregulation, inflammation and an uncoordinated adaptive immune response to SARS-CoV-2","volume":"25","author":"Yin","year":"2024","journal-title":"Nat Immunol"},{"key":"2026102110244910400_kxag013-B44","first-page":"243","article-title":"Confidence intervals for high-dimensional cox models","volume":"31","author":"Yu","year":"2021","journal-title":"Stat Sinica"},{"key":"2026102110244910400_kxag013-B45","first-page":"2772","volume-title":"Workshop on Very High Dimensional Semiparametric Models (Report No. 48\/2011)","author":"Zhang","year":"2011"},{"key":"2026102110244910400_kxag013-B46","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/rssb.12026","article-title":"Confidence intervals for low dimensional parameters in high dimensional linear models","volume":"76","author":"Zhang","year":"2014","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"key":"2026102110244910400_kxag013-B47","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.1080\/01621459.2023.2206084","article-title":"Estimation of linear functionals in high dimensional linear models: from sparsity to non-sparsity","volume":"119","author":"Zhao","year":"2024","journal-title":"J Am Stat Assoc"},{"key":"2026102110244910400_kxag013-B48","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1111\/biom.12418","article-title":"A significance test for graph-constrained estimation","volume":"72","author":"Zhao","year":"2016","journal-title":"Biometrics"},{"key":"2026102110244910400_kxag013-B49","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1214\/20-STS815","article-title":"In defense of the indefensible: a very naive approach to high-dimensional inference","volume":"36","author":"Zhao","year":"2021","journal-title":"Statistical Science"},{"key":"2026102110244910400_kxag013-B50","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1080\/01621459.2017.1356319","article-title":"Linear hypothesis testing in dense high-dimensional linear models","volume":"113","author":"Zhu","year":"2018","journal-title":"J Am Stat Assoc"}],"container-title":["Biostatistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/27\/1\/kxag013\/68223061\/kxag013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/27\/1\/kxag013\/68223061\/kxag013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T14:24:57Z","timestamp":1792592697000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biostatistics\/article\/doi\/10.1093\/biostatistics\/kxag013\/8669989"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1,20]]}},"URL":"https:\/\/doi.org\/10.1093\/biostatistics\/kxag013","relation":{},"ISSN":["1465-4644","1468-4357"],"issn-type":[{"value":"1465-4644","type":"print"},{"value":"1468-4357","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,1]]},"published":{"date-parts":[[2026,1]]},"article-number":"kxag013"}}