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In this article, we propose a novel nonparametric Bayesian Q-learning approach to construct optimal sequential treatment regimes that adjust for partial compliance. We consider the popular potential compliance framework, where some potential compliances are latent and need to be imputed. The key challenge is learning the joint distribution of the potential compliances, which we accomplish using a Dirichlet process mixture model. Our approach provides two kinds of treatment regimes: (1) conditional regimes that depend on the potential compliance values; and (2) marginal regimes where the potential compliances are marginalized. Extensive simulation studies highlight the usefulness of our method compared to intention-to-treat analyses. We apply our method to the Adaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) study , where the goal is to construct optimal treatment regimes to engage patients in therapy. <\/jats:p>","DOI":"10.1177\/09622802231181223","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T07:02:29Z","timestamp":1686898949000},"page":"1649-1663","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Nonparametric Bayesian Q-learning for optimization of dynamic treatment regimes in the presence of partial compliance"],"prefix":"10.1177","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4567-0027","authenticated-orcid":false,"given":"Indrabati","family":"Bhattacharya","sequence":"first","affiliation":[{"name":"Department of Statistics, Florida State University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2611-9512","authenticated-orcid":false,"given":"Ashkan","family":"Ertefaie","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology, University of Rochester, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0426-0323","authenticated-orcid":false,"given":"Kevin G","family":"Lynch","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Pennsylvania, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James R","family":"McKay","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Pennsylvania, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brent A","family":"Johnson","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology, University of Rochester, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"key":"bibr1-09622802231181223","doi-asserted-by":"publisher","DOI":"10.1037\/11888-000"},{"key":"bibr2-09622802231181223","doi-asserted-by":"publisher","DOI":"10.1007\/s11920-012-0296-5"},{"key":"bibr3-09622802231181223","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7428-9"},{"key":"bibr4-09622802231181223","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974188"},{"key":"bibr5-09622802231181223","unstructured":"Watkins C. 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