{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T20:32:27Z","timestamp":1786480347378,"version":"build-2736575974"},"reference-count":43,"publisher":"Wiley","issue":"10-12","license":[{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"vor","delay-in-days":17,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["1R01HL159077"],"award-info":[{"award-number":["1R01HL159077"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006093","name":"Patient-Centered Outcomes Research Institute","doi-asserted-by":"publisher","award":["ME\u20102021C2\u201023685"],"award-info":[{"award-number":["ME\u20102021C2\u201023685"]}],"id":[{"id":"10.13039\/100006093","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Selecting important individual\u2010 and cluster\u2010level predictors has become increasingly critical in healthcare research, where data often exhibit hierarchical structures due to collection from multiple clusters. Mixed\u2010effects models, which account for within\u2010cluster correlation and between\u2010cluster heterogeneity, are a natural approach for multilevel variable selection. However, currently available variable selection methods for multilevel data are predominantly based on mixed\u2010effects models that impose restrictive parametric assumptions, potentially limiting their utility when the underlying relationships are nonlinear or involve interactions. While nonparametric methods have shown promise for variable selection in non\u2010clustered data, they have been much less studied in the multilevel setting. Moreover, nonparametric methods that explicitly account for multilevel structure have largely been designed for prediction, rather than for simultaneous selection of relevant covariates at both the individual and cluster levels. To address these limitations, we propose a flexible, fully Bayesian unified framework for simultaneous variable selection of both fixed and random effects. Our framework integrates the nonparametric flexibility of Bayesian Additive Regression Trees (BART) for fixed\u2010effect predictor selection with a hierarchical Bayesian component that identifies random\u2010effect predictors via covariance decomposition and permutation strategies. To address scenarios common in multilevel data, where cluster\u2010level covariates are constant within clusters and can induce near\u2010collinearity and instability in selection, we further propose a computationally efficient two\u2010step procedure. This method disentangles the contributions of individual\u2010 and cluster\u2010level predictors, thereby mitigating collinearity and improving stability in variable selection. Comprehensive simulation studies demonstrate the effectiveness and robustness of our proposed methods across diverse scenarios. We further illustrate the practical utility of these approaches by applying them to a multilevel Alzheimer's disease dataset.<\/jats:p>","DOI":"10.1002\/sim.70593","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T01:34:26Z","timestamp":1779154466000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi\u2010Level Variable Selection Using a\n                    <scp>BART<\/scp>\n                    \u2010Enhanced Mixed\u2010Effects Framework"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5495-0058","authenticated-orcid":false,"given":"Keming","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Biostatistics Brown University  Providence Rhode Island USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaoyao","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology Rutgers University  Piscataway New Jersey USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5221-1489","authenticated-orcid":false,"given":"Jungang","family":"Zou","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Columbia University  New York New York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sijian","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics Rutgers University  Piscataway New Jersey USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernadette A.","family":"Fausto","sequence":"additional","affiliation":[{"name":"Center for Molecular and Behavioral Neuroscience Rutgers University  Newark New Jersey USA"},{"name":"Department of Health Science &amp; Clinical Practice Thomas Jefferson University  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liangyuan","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology Rutgers University  Piscataway New Jersey USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,5,18]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010933404324"},{"key":"e_1_2_10_3_1","doi-asserted-by":"crossref","unstructured":"T.ChenandC.Guestrin \u201cXGBoost: A Scalable Tree Boosting System \u201dProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2016) 785\u2013794.","DOI":"10.1145\/2939672.2939785"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOAS285"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOAS755"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802211046385"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-022-01608-7"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.202200178"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/23-STS900"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8924"},{"key":"e_1_2_10_11_1","unstructured":"B.Wundervald A.Parnell andK.Domijan \u201cHierarchical Embedded Bayesian Additive Regression Trees \u201darXiv preprint 2022."},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9548"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2010.01391.x"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2012.02.005"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1215989"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2003.00089.x"},{"key":"e_1_2_10_17_1","volume-title":"Bayesian Variable Selection for Random Intercept Modeling of Gaussian and Non\u2010Gaussian Data","author":"Fr\u00fchwirth\u2010Schnatter S.","year":"2010"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v043.i14"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1264957"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1998.10473750"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/16-BA999"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13176"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v097.i01"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8347"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000409"},{"issue":"2","key":"e_1_2_10_26_1","first-page":"205","article-title":"Variable Selection for Generalized Linear Mixed Models by L1\u2010Penalized Estimation","volume":"20","author":"Groll A.","year":"2010","journal-title":"Statistics and Computing"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2012.741599"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-011-5258-3"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v080.i01"},{"key":"e_1_2_10_30_1","doi-asserted-by":"publisher","DOI":"10.32614\/RJ-2018-017"},{"key":"e_1_2_10_31_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478694"},{"key":"e_1_2_10_32_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1993.10476353"},{"issue":"2","key":"e_1_2_10_33_1","first-page":"339","article-title":"Approaches for Bayesian Variable Selection","volume":"7","author":"George E. 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