{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:39:42Z","timestamp":1791308382732,"version":"4.3.1"},"reference-count":23,"publisher":"Wiley","issue":"21","license":[{"start":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T00:00:00Z","timestamp":1657152000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2022,9,20]]},"abstract":"<jats:p>Personalized medicine, a paradigm of medicine tailored to a patient's characteristics, is an increasingly attractive field in health care. An important goal of personalized medicine is to identify a subgroup of patients, based on baseline covariates, that benefits more from the targeted treatment than other comparative treatments. Most of the current subgroup identification methods only focus on obtaining a subgroup with an enhanced treatment effect without paying attention to subgroup size. Yet, a clinically meaningful subgroup learning approach should identify the maximum number of patients who can benefit from the better treatment. In this article, we present an optimal subgroup selection rule (SSR) that maximizes the number of selected patients, and in the meantime, achieves the pre\u2010specified clinically meaningful mean outcome, such as the average treatment effect. We derive two equivalent theoretical forms of the optimal SSR based on the contrast function that describes the treatment\u2010covariates interaction in the outcome. We further propose a constrained policy tree search algorithm (CAPITAL) to find the optimal SSR within the interpretable decision tree class. The proposed method is flexible to handle multiple constraints that penalize the inclusion of patients with negative treatment effects, and to address time to event data using the restricted mean survival time as the clinically interesting mean outcome. Extensive simulations, comparison studies, and real data applications are conducted to demonstrate the validity and utility of our method.<\/jats:p>","DOI":"10.1002\/sim.9507","type":"journal-article","created":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T04:09:31Z","timestamp":1657253371000},"page":"4227-4244","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["CAPITAL: Optimal subgroup identification via constrained\u00a0policy tree search"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5679-8862","authenticated-orcid":false,"given":"Hengrui","family":"Cai","sequence":"first","affiliation":[{"name":"Department of Statistics University of California Irvine  Irvine California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7320-4755","authenticated-orcid":false,"given":"Wenbin","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Statistics North Carolina State University  Raleigh North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rachel","family":"Marceau West","sequence":"additional","affiliation":[{"name":"Biostatistics and Research Decision Sciences Merck &amp; Co., Inc.  North Wales Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0316-7362","authenticated-orcid":false,"given":"Devan V.","family":"Mehrotra","sequence":"additional","affiliation":[{"name":"Biostatistics and Research Decision Sciences Merck &amp; Co., Inc.  North Wales Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingkang","family":"Huang","sequence":"additional","affiliation":[{"name":"Biostatistics and Research Decision Sciences Merck &amp; Co., Inc.  Rahway New Jersey USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,7,7]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-statistics-030718-105251"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/widm.1326"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2004.00242.x"},{"issue":"2","key":"e_1_2_9_5_1","first-page":"141","article-title":"Subgroup analysis via recursive partitioning","volume":"10","author":"Su X","year":"2009","journal-title":"J Mach Learn Res"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4322"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxq060"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4108"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOAS593"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6454"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6920"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7064"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1097\/EDE.0000000000000991"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1303386"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2019.1660169"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxz026"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9253"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA15732"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344064"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2017.1356325"},{"key":"e_1_2_9_21_1","unstructured":"ZhouZ AtheyS WagerS.Offline multi\u2010action policy learning: generalization and optimization. arXiv preprint arXiv:1810.04778 2018."},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-016-9376-x"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199610103351501"},{"key":"e_1_2_9_24_1","unstructured":"KennedyEH.Optimal doubly robust estimation of heterogeneous causal effects. arXiv preprint arXiv:2004.14497 2020."}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.9507","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.9507","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.9507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T09:44:41Z","timestamp":1692783881000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.9507"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,7]]},"references-count":23,"journal-issue":{"issue":"21","published-print":{"date-parts":[[2022,9,20]]}},"alternative-id":["10.1002\/sim.9507"],"URL":"https:\/\/doi.org\/10.1002\/sim.9507","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,7]]},"assertion":[{"value":"2021-10-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-06-06","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-07-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}