{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T00:15:58Z","timestamp":1783556158568,"version":"3.55.0"},"reference-count":34,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T00:00:00Z","timestamp":1780617600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371276"],"award-info":[{"award-number":["12371276"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371281"],"award-info":[{"award-number":["12371281"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:p>\n                    Interactions and correlations among features are essential in biology, as well as in other fields. This article introduces a novel approach for linear interaction models characterized by complex correlation structures. By integrating local linear approximation and Laplacian smoothing penalty with\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>l<\/mml:mi>\n                          <mml:mn>1<\/mml:mn>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    or\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>l<\/mml:mi>\n                          <mml:mn>1<\/mml:mn>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>l<\/mml:mi>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    penalties, our methods effectively estimate and predict highly correlated interaction models. Theoretical analysis confirms that both methods converge to an oracle solution within two iterations, demonstrating a rapid convergence rate. In simulation studies, our proposed methods outperform existing techniques in terms of prediction accuracy, estimation precision, and variable selection. When applied to protein microarray data for Alzheimer\u2019s disease analysis, they reveal substantial main and interaction effects with notably lower prediction errors. This highlights the potential of our methods as powerful tools for analyzing linear interaction models with intricate correlations, applicable across a wide range of biological research and other fields.\n                  <\/jats:p>","DOI":"10.1177\/09622802261457286","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T08:29:49Z","timestamp":1780648189000},"page":"1480-1492","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["An effective method for modeling highly correlated interaction models with applications in Alzheimer\u2019s disease\u00a0analysis"],"prefix":"10.1177","volume":"35","author":[{"given":"Shun","family":"Yu","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yujie","family":"Gai","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8321-6859","authenticated-orcid":false,"given":"Yuehan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,6,5]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.2174\/1389202919666171218162210"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2021.1917419"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"e_1_3_2_5_2","first-page":"1","article-title":"Optimization with sparsity-inducing penalties","volume":"4","author":"Bach F","year":"2012","unstructured":"Bach F, Jenatton R, Mairal J, et al. 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