{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T16:57:42Z","timestamp":1791392262334,"version":"4.3.3"},"reference-count":38,"publisher":"Institute of Mathematical Statistics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Appl. Stat."],"published-print":{"date-parts":[[2025,9,1]]},"abstract":"<jats:p>Contrastive dimension reduction methods have been developed for case-control study data to identify variation that is enriched in the foreground (case) data X relative to the background (control) data Y. Here we develop contrastive regression for the setting where there is a response variable r associated with each foreground observation. This situation occurs frequently when, for example, the unaffected controls do not have a disease grade or intervention dosage, but the affected cases have a disease grade or intervention dosage, as in autism severity, solid tumors stages, polyp sizes, or warfarin dosages. Our contrastive regression model captures shared low-dimensional variation between the predictors in the case and control groups and then explains the case-specific response variables through the variance that remains in the predictors after shared variation is removed. We show that, in one single-cell RNA sequencing dataset on cellular differentiation in chronic rhinosinusitis with and without nasal polyps and in another single-nucleus RNA sequencing dataset on autism severity in postmortem brain samples from donors with and without autism, our contrastive linear regression performs feature ranking and identifies biologically-informative predictors associated with response that cannot be identified using other approaches.<\/jats:p>","DOI":"10.1214\/24-aoas1977","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T11:48:25Z","timestamp":1756381705000},"page":"1868-1883","source":"Crossref","is-referenced-by-count":2,"title":["Contrastive linear regression"],"prefix":"10.1214","volume":"19","author":[{"given":"Boyang","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Genetics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sarah","family":"Nyquist","sequence":"additional","affiliation":[{"name":"Gladstone Institutes"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Jones","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6139-7334","authenticated-orcid":false,"given":"Barbara E.","family":"Engelhardt","sequence":"additional","affiliation":[{"name":"Gladstone Institutes and Department of Biomedical Data Science, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9146-705X","authenticated-orcid":false,"given":"Didong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of North Carolina at Chapel Hill"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"16","doi-asserted-by":"publisher","unstructured":"<small>Kanehisa, M.<\/small> and <small>Goto, S.<\/small> (2000). 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