{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:25:33Z","timestamp":1740133533593,"version":"3.37.3"},"reference-count":75,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T00:00:00Z","timestamp":1704844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS 2210640","DMS 1952406"],"award-info":[{"award-number":["DMS 2210640","DMS 1952406"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The individualized treatment rule (ITR), which recommends an optimal treatment based on individual characteristics, has drawn considerable interest from many areas such as precision medicine, personalized education, and personalized marketing. Existing ITR estimation methods mainly adopt 1 of 2 or more treatments. However, a combination of multiple treatments could be more powerful in various areas. In this paper, we propose a novel double encoder model (DEM) to estimate the ITR for combination treatments. The proposed double encoder model is a nonparametric model which not only flexibly incorporates complex treatment effects and interaction effects among treatments but also improves estimation efficiency via the parameter-sharing feature. In addition, we tailor the estimated ITR to budget constraints through a multi-choice knapsack formulation, which enhances our proposed method under restricted-resource scenarios. In theory, we provide the value reduction bound with or without budget constraints, and an improved convergence rate with respect to the number of treatments under the DEM. Our simulation studies show that the proposed method outperforms the existing ITR estimation in various settings. We also demonstrate the superior performance of the proposed method in patient-derived xenograft data that recommends optimal combination treatments to shrink the tumour size of the colorectal cancer.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad141","type":"journal-article","created":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T18:30:43Z","timestamp":1704911443000},"page":"714-741","source":"Crossref","is-referenced-by-count":0,"title":["Optimal individualized treatment rule for combination treatments under budget constraints"],"prefix":"10.1093","volume":"86","author":[{"given":"Qi","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Statistics, University of California Irvine , Irvine ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoda","family":"Fu","sequence":"additional","affiliation":[{"name":"Eli Lilly and Company , Indianapolis 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