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Machine learning (ML) is extensively applied to diagnose medical diseases due to its high accuracy and ease of implementation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>The microarray expression dataset (GSE83421) was selected from the Gene Expression Omnibus Database (GEO) for analysis. Differential expression analysis was performed with false discovery rate (FDR) correction. Weighted gene co-expression network analysis (WGCNA) identified correlated gene modules. Consensus feature selection using six algorithms (LASSO, SVM-RFE, random forest, Boruta, XGBoost, and decision tree) was applied to identify robust biomarkers and mitigate overfitting. A penalized logistic regression model was developed and evaluated using leave-one-out cross-validation (LOOCV).<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Ten candidate genes were identified by intersecting 24 DEGs with the WGCNA red module. Consensus ML selected five hub genes (LOC51092, KIAA1479, PRO2214, TBX4, and ZNF361). T. The LOOCV-validated penalized logistic regression model effectively distinguished PHPT from normal controls.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>Our analysis identified a 5-gene signature (LOC51092, KIAA1479, PRO2214, TBX4, and ZNF361) with diagnostic potential for PHPT. The model was internally validated using LOOCV. However, without nested feature selection or external validation, the reported performance likely represents an optimistic estimate. Given the limited sample size, these findings represent preliminary hypotheses for PHPT diagnosis, requiring validation in independent cohorts.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1007\/s42000-026-00832-w","type":"journal-article","created":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T15:32:03Z","timestamp":1792423923000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Machine learning and penalized logistic regression-based models for the identification of potential characteristic genes in primary hyperparathyroidism"],"prefix":"10.1007","author":[{"given":"Tianze","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qila","family":"Sa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boyuan","family":"Nan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,19]]},"reference":[{"key":"832_CR1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1038\/nrendo.2017.104","volume":"14","author":"MD Walker","year":"2018","unstructured":"Walker MD, Silverberg SJ (2018) Primary hyperparathyroidism. 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Users can download relevant data for research free of charge and publish relevant articles. Since our study is based on open source data, there are no ethical issues or other conflicts of interest.","order":1,"name":"Ethics","label":"Ethical approval and consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":3,"name":"Ethics","label":"Clinical trial number","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.","order":4,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}]}}