{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T22:25:55Z","timestamp":1761171955416,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T00:00:00Z","timestamp":1760745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Complex human diseases, including cancer, are linked to genetic factors. Genome-wide association studies (GWASs) are powerful for identifying genetic variants associated with cancer but are limited by their reliance on case\u2013control data. We propose approaches to expanding GWAS by using tumor and paired normal tissues to investigate somatic mutations. We apply penalized maximum likelihood estimation for single-marker analysis and develop a Bayesian hierarchical model to integrate multiple markers, identifying SNP sets grouped by genes or pathways, improving detection of moderate-effect SNPs. Applied to breast cancer data from The Cancer Genome Atlas (TCGA), both single- and multiple-marker analyses identify associated genes, with multiple-marker analysis providing more consistent results with external resources. The Bayesian model significantly increases the chance of new discoveries.<\/jats:p>","DOI":"10.3390\/e27101077","type":"journal-article","created":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T08:18:54Z","timestamp":1760948334000},"page":"1077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bayesian Model for Paired Data in Genome-Wide Association Studies with Application to Breast Cancer"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7024-405X","authenticated-orcid":false,"given":"Yashi","family":"Bu","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0676-3143","authenticated-orcid":false,"given":"Min","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9344-8493","authenticated-orcid":false,"given":"Zhenyu","family":"Xuan","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8561-6511","authenticated-orcid":false,"given":"Xinlei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Smith, J.E., Clark, A.R., and Staggemeier, A.T. 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