{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:34:40Z","timestamp":1791390880682,"version":"4.3.3"},"reference-count":61,"publisher":"Wiley","issue":"15-17","license":[{"start":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T00:00:00Z","timestamp":1783555200000},"content-version":"vor","delay-in-days":8,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["200021_219384"],"award-info":[{"award-number":["200021_219384"]}],"id":[{"id":"10.13039\/501100001711","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":[[2026,7]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Accurate diagnostic tests are essential for effective screening and treatment. However, individual biomarkers often fail to provide sufficient diagnostic accuracy, as they typically capture only one aspect of the complex disease process. Combining multiple biomarkers, each capturing a distinct mechanism, can help construct more informative diagnostic tests. In practice, logistic regression is used as the default to combine biomarkers, but it can perform poorly when biomarker distributions exhibit skewness or differ across disease groups. Nonparametric methods provide more flexibility but generally require large sample sizes that are infrequently available in biomedical research. We propose a novel framework called transformation discriminant analysis which combines biomarkers through the likelihood ratio function to construct theoretically optimal diagnostic scores. Transformation discriminant analysis (TDA)\u00a0balances between flexibility and efficiency. It can accommodate a wide range of distributional shapes and disease\u2010specific dependence structures while remaining fully parametric. This allows for likelihood inference and strong performance even in small\u2010sample settings. We evaluate TDA through simulations and benchmark its performance against commonly used methods. Finally, we illustrate its utility in constructing an optimal diagnostic test for hepatocellular carcinoma, a disease with no single ideal biomarker. An open\u2010source R implementation is provided for reproducibility and broader application.<\/jats:p>","DOI":"10.1002\/sim.70665","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T16:07:58Z","timestamp":1783613278000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Transformation Discriminant Analysis for Constructing Optimal Biomarker Combinations"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1858-9987","authenticated-orcid":false,"given":"Ainesh","family":"Sewak","sequence":"first","affiliation":[{"name":"Department of Clinical Research Universit\u00e4t Bern  Bern Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7312-1001","authenticated-orcid":false,"given":"Sandra","family":"Siegfried","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Epidemiologie, Biostatistik Und Pr\u00e4vention Universit\u00e4t Z\u00fcrich  Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8301-0471","authenticated-orcid":false,"given":"Torsten","family":"Hothorn","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Epidemiologie, Biostatistik Und Pr\u00e4vention Universit\u00e4t Z\u00fcrich  Z\u00fcrich Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,9]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2431"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.15252\/emmm.202216061"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1993.10476417"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/1.2.123"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4238"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6046"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280213481053"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6956"},{"key":"e_1_2_11_10_1","volume-title":"Signal Detection Theory and Psychophysics","author":"Green D. M.","year":"1966"},{"key":"e_1_2_11_11_1","volume-title":"Signal Detection Theory and ROC Analysis","author":"Egan J. P.","year":"1975"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006\u2010341x.2002.00657.x"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7535"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/22\u2010aos2210"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/90.2.379"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhep.2005.03.019"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dld.2018.08.019"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0151069"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541\u20100420.2005.00420.x"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1186\/1756\u20100500\u20107\u201025"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198509844.001.0001"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.2307\/2285453"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.2307\/2287404"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.2307\/2286261"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.495"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4068"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2015.1066681"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10182\u2010020\u201000388\u2010z"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1214\/12\u2010sts391"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201400043"},{"key":"e_1_2_11_31_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8047"},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.10026"},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.1111\/sjos.12501"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1080\/00031305.2023.2203177"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800310310"},{"key":"e_1_2_11_36_1","doi-asserted-by":"publisher","DOI":"10.2307\/2346911"},{"key":"e_1_2_11_37_1","doi-asserted-by":"publisher","DOI":"10.1111\/sjos.12291"},{"key":"e_1_2_11_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2012.03.001"},{"key":"e_1_2_11_39_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v092.i01"},{"key":"e_1_2_11_40_1","unstructured":"T.Hothorn \u201cOn Nonparanormal Likelihoods \u201d(2024). arXiv:2408.17346 [stat.ME]."},{"key":"e_1_2_11_41_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802231176030"},{"key":"e_1_2_11_42_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802261445416"},{"key":"e_1_2_11_43_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517\u20106161.1996.tb02080.x"},{"key":"e_1_2_11_44_1","doi-asserted-by":"publisher","DOI":"10.5061\/dryad.3n901"},{"key":"e_1_2_11_45_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12072\u2010007\u20109038\u2010x"},{"key":"e_1_2_11_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/s1089\u20103261(05)70158\u20106"},{"key":"e_1_2_11_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cgh.2013.09.053"},{"key":"e_1_2_11_48_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.916577"},{"key":"e_1_2_11_49_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729394"},{"key":"e_1_2_11_50_1","doi-asserted-by":"crossref","unstructured":"T.Hothorn S.Siegfried andL.Kook \u201ctram: Transformation Models. Comprehensive R Archive Network \u201d(2026) Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.tram.","DOI":"10.32614\/CRAN.package.tram"},{"key":"e_1_2_11_51_1","doi-asserted-by":"crossref","unstructured":"A.Genz F.Bretz T.Miwa X.Mi andT.Hothorn \u201cmvtnorm: Multivariate Normal and t Distributions \u201d(2026) Comprehensive R Archive Network; Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.mvtnorm.","DOI":"10.32614\/CRAN.package.mvtnorm"},{"key":"e_1_2_11_52_1","doi-asserted-by":"crossref","unstructured":"H. W.Borchers \u201cpracma: Practical Numerical Math Functions. Comprehensive R Archive Network \u201dVienna Austria: (2025) https:\/\/doi.org\/10.32614\/CRAN.package.pracma.","DOI":"10.32614\/CRAN.package.pracma"},{"key":"e_1_2_11_53_1","doi-asserted-by":"crossref","unstructured":"M.HofertandC.Lemieux \u201cqrng: (Randomized) Quasi\u2010Random Number Generators \u201d(2026) Comprehensive R Archive Network; Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.qrng.","DOI":"10.32614\/CRAN.package.qrng"},{"key":"e_1_2_11_54_1","doi-asserted-by":"crossref","unstructured":"B.Tamasi \u201ctramME: Transformation Models With Mixed Effects \u201d(2025) Comprehensive R Archive Network; Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.tramME.","DOI":"10.32614\/CRAN.package.tramME"},{"key":"e_1_2_11_55_1","doi-asserted-by":"crossref","unstructured":"S.Wood \u201cmgcv: Mixed GAM Computation Vehicle With Automatic Smoothness Estimation. Comprehensive R Archive Network \u201d(2025) Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.mgcv.","DOI":"10.32614\/CRAN.package.mgcv"},{"key":"e_1_2_11_56_1","doi-asserted-by":"crossref","unstructured":"M.Hofert I.Kojadinovic M.Maechler andJ.Yan \u201ccopula: Multivariate Dependence With Copulas. Comprehensive R Archive Network; Vienna Austria \u201d(2026) https:\/\/doi.org\/10.32614\/CRAN.package.copula.","DOI":"10.32614\/CRAN.package.copula"},{"key":"e_1_2_11_57_1","doi-asserted-by":"crossref","unstructured":"L.Breiman A.Cutler A.Liaw andM.Wiener \u201crandomForest: Breiman and Cutlers Random Forests for Classification and Regression. Comprehensive R Archive Network \u201d(2024) Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.randomForest.","DOI":"10.32614\/CRAN.package.randomForest"},{"key":"e_1_2_11_58_1","doi-asserted-by":"crossref","unstructured":"T.Chen T.He M.Benesty et al. \u201cxgboost: Extreme Gradient Boosting. Comprehensive R Archive Network \u201d(2026) Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.xgboost.","DOI":"10.32614\/CRAN.package.xgboost"},{"key":"e_1_2_11_59_1","doi-asserted-by":"crossref","unstructured":"B.RipleyandB.Venables \u201cMASS: Support Functions and Datasets for Venables and Ripley's MASS \u201d(2025) Comprehensive R Archive Network; Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.MASS.","DOI":"10.32614\/CRAN.package.MASS"},{"key":"e_1_2_11_60_1","doi-asserted-by":"crossref","unstructured":"T.HastieandR.Tibshirani \u201cmda:Mixture and Flexible Discriminant Analysis \u201d(2024) Comprehensive R Archive Network; Vienna Austria https:\/\/doi.org\/10.32614\/CRAN.package.mda.","DOI":"10.32614\/CRAN.package.mda"},{"key":"e_1_2_11_61_1","doi-asserted-by":"crossref","unstructured":"R Core Team \u201cR: A Language and Environment for Statistical Computing \u201d(2026) R Foundation for Statistical Computing; Vienna Austria https:\/\/doi.org\/10.32614\/R.manuals.","DOI":"10.32614\/R.manuals"},{"key":"e_1_2_11_62_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v114.i11"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70665","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70665","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70665","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T15:55:05Z","timestamp":1784649305000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":61,"journal-issue":{"issue":"15-17","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["10.1002\/sim.70665"],"URL":"https:\/\/doi.org\/10.1002\/sim.70665","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"2025-06-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-06-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-09","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70665"}}