{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T17:58:15Z","timestamp":1790791095765,"version":"4.1.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,3,29]],"date-time":"2023-03-29T00:00:00Z","timestamp":1680048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","award":["FT190100374"],"award-info":[{"award-number":["FT190100374"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Clinicians often make sequences of treatment decisions that can be framed as dynamic treatment regimes. In this paper, we propose a Bayesian likelihood-based dynamic treatment regime model that incorporates regression specifications to yield interpretable relationships between covariates and stage-wise outcomes. We define a set of probabilistically-coherent properties for dynamic treatment regime processes and present the theoretical advantages that are consequential to these properties. We justify the likelihood-based approach by showing that it guarantees these probabilistically-coherent properties, whereas existing methods lead to process spaces that typically violate these properties and lead to modelling assumptions that are infeasible. Through a numerical study, we show that our proposed method can achieve superior performance over existing state-of-the-art methods.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad016","type":"journal-article","created":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T05:03:48Z","timestamp":1680152628000},"page":"551-574","source":"Crossref","is-referenced-by-count":4,"title":["Bayesian likelihood-based regression for estimation of optimal dynamic treatment regimes"],"prefix":"10.1093","volume":"85","author":[{"given":"Weichang","family":"Yu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, The University of Melbourne , Melbourne , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7743-0840","authenticated-orcid":false,"given":"Howard D","family":"Bondell","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, The University of Melbourne , Melbourne , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,3,29]]},"reference":[{"issue":"2","key":"2023071211302927300_qkad016-B1","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.2202\/1557-4679.1204","article-title":"Optimal dynamic regimes: Presenting a case for predictive inference","volume":"6","author":"Arjas","year":"2010","journal-title":"The International Journal of Biostatistics"},{"key":"2023071211302927300_qkad016-B2","volume-title":"Dynamic programming","author":"Bellman","year":"1957","edition":"1st ed."},{"issue":"518","key":"2023071211302927300_qkad016-B3","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2023071211302927300_qkad016-B4","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1111\/biom.12052","article-title":"Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme","volume":"69","author":"Chakraborty","year":"2013","journal-title":"Biometrics"},{"issue":"3","key":"2023071211302927300_qkad016-B5","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1177\/0962280209105013","article-title":"Inference for non-regular parameters in optimal dynamic treatment regimes","volume":"19","author":"Chakraborty","year":"2010","journal-title":"Statistical Methods in Medical Research"},{"issue":"2","key":"2023071211302927300_qkad016-B6","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1111\/sjos.12359","article-title":"A smoothed Q-learning algorithm for estimating optimal dynamic treatment regimes","volume":"46","author":"Fan","year":"2019","journal-title":"Scandinavian Journal of Statistics"},{"issue":"3","key":"2023071211302927300_qkad016-B7","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1080\/10618600.2014.926819","article-title":"Fast and stable multiple smoothing parameter selection in smoothing splines analysis of variance model with large samples","volume":"24","author":"Helwig","year":"2015","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"4","key":"2023071211302927300_qkad016-B8","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1111\/j.1541-0420.2009.01368.x","article-title":"Regression for optimal dynamic treatment regimes","volume":"66","author":"Henderson","year":"2010","journal-title":"Biometrics"},{"issue":"26","key":"2023071211302927300_qkad016-B9","doi-asserted-by":"crossref","first-page":"3424","DOI":"10.1002\/sim.6558","article-title":"Optimization of multi-stage dynamic treatment regimes utilizing accumulated data","volume":"34","author":"Huang","year":"2015","journal-title":"Statistics in Medicine"},{"issue":"1","key":"2023071211302927300_qkad016-B10","first-page":"1225","article-title":"Dynamic treatment regimes: Technical challenges and applications","volume":"8","author":"Laber","year":"2014","journal-title":"Electronic Journal of Statistics"},{"issue":"518","key":"2023071211302927300_qkad016-B11","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1080\/01621459.2016.1155993","article-title":"Interactive Q-learning for quantiles","volume":"112","author":"Linn","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"2023071211302927300_qkad016-B12","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1038\/s41598-018-37142-0","article-title":"Learning the dynamic treatment regimes from medical registry data through deep Q-network","volume":"9","author":"Liu","year":"2019","journal-title":"Scientific Reports"},{"issue":"2","key":"2023071211302927300_qkad016-B13","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s12561-013-9103-z","article-title":"Q-learning: Flexible learning about useful utilities","volume":"6","author":"Moodie","year":"2014","journal-title":"Statistics in Biosciences"},{"issue":"1","key":"2023071211302927300_qkad016-B14","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1111\/j.1467-9469.2009.00661.x","article-title":"Estimating optimal dynamic regimes: Correcting bias under the null","volume":"37","author":"Moodie","year":"2010","journal-title":"Scandinavian Journal of Statistics"},{"issue":"2","key":"2023071211302927300_qkad016-B15","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1111\/1467-9868.00389","article-title":"Optimal dynamic treatment regimes","volume":"65","author":"Murphy","year":"2003","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"2023071211302927300_qkad016-B16","first-page":"1073","article-title":"A generalization error for Q-learning","volume":"6","author":"Murphy","year":"2005","journal-title":"Journal of Machine Learning Research"},{"issue":"10","key":"2023071211302927300_qkad016-B17","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1002\/sim.2022","article-title":"An experiment design for the development of adaptive treatment strategies","volume":"24","author":"Murphy","year":"2005","journal-title":"Statistics in Medicine"},{"issue":"456","key":"2023071211302927300_qkad016-B18","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1198\/016214501753382327","article-title":"Marginal mean models for dynamic regimes","volume":"96","author":"Murphy","year":"2001","journal-title":"Journal of the American Statistical Association"},{"issue":"523","key":"2023071211302927300_qkad016-B19","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1080\/01621459.2017.1340887","article-title":"A Bayesian machine learning approach for optimizing dynamic treatment regimes","volume":"113","author":"Murray","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"2023071211302927300_qkad016-B20","first-page":"8","article-title":"Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, Part I: Main content","volume":"6","author":"Orellana","year":"2010","journal-title":"International Journal of Biostatistics"},{"issue":"2","key":"2023071211302927300_qkad016-B21","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1198\/tast.2010.09058","article-title":"Explaining variational approximations","volume":"64","author":"Ormerod","year":"2010","journal-title":"The American Statistician"},{"key":"2023071211302927300_qkad016-B22","first-page":"1393","article-title":"A new approach to causal inference in mortality studies with sustained exposure periods\u2014Application to control of the healthy worker survivor effect","volume":"7","author":"Robins","year":"1986","journal-title":"Computers & Mathematics with Applications"},{"key":"2023071211302927300_qkad016-B23","first-page":"68","volume-title":"Latent variable modeling and applications to causality","author":"Robins","year":"1997"},{"key":"2023071211302927300_qkad016-B24","volume-title":"Proceedings of the second Seattle symposium in biostatistics","author":"Robins","year":"2004"},{"issue":"23","key":"2023071211302927300_qkad016-B25","doi-asserted-by":"crossref","first-page":"4678","DOI":"10.1002\/sim.3301","article-title":"Estimation and extrapolation of optimal treatment and testing strategies","volume":"27","author":"Robins","year":"2008","journal-title":"Statistics in Medicine"},{"issue":"4","key":"2023071211302927300_qkad016-B26","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1214\/13-STS450","article-title":"Q-learning and A-learning methods for estimating optimal dynamic treatment regimes","volume":"29","author":"Schulte","year":"2014","journal-title":"Statistical Science"},{"issue":"531","key":"2023071211302927300_qkad016-B27","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1080\/01621459.2019.1629939","article-title":"Estimating optimal dynamic treatment regimes with survival outcomes","volume":"115","author":"Simoneau","year":"2019","journal-title":"Journal of the American Statistical Association"},{"issue":"5","key":"2023071211302927300_qkad016-B28","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.amepre.2007.12.024","article-title":"Web-based smoking cessation components and tailoring depth: Results of a randomized trial","volume":"34","author":"Strecher","year":"2008","journal-title":"American Journal of Preventive Medicine"},{"issue":"533","key":"2023071211302927300_qkad016-B29","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1080\/01621459.2020.1819294","article-title":"Stochastic tree search for estimating optimal dynamic treatment regimes","volume":"116","author":"Sun","year":"2021","journal-title":"Journal of the American Statistical Association"},{"issue":"457","key":"2023071211302927300_qkad016-B30","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1198\/016214502753479202","article-title":"Selecting therapeutic strategies based on efficacy and death in multicourse clinical trials","volume":"97","author":"Thall","year":"2002","journal-title":"Journal of the American Statistical Association"},{"issue":"26","key":"2023071211302927300_qkad016-B31","doi-asserted-by":"crossref","first-page":"4687","DOI":"10.1002\/sim.2894","article-title":"Bayesian and frequentist two-stage treatment strategies based on sequential failure times subject to interval censoring","volume":"26","author":"Thall","year":"2007","journal-title":"Statistics in Medicine"},{"issue":"393","key":"2023071211302927300_qkad016-B32","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1080\/01621459.1986.10478240","article-title":"Accurate approximations for posterior moments and marginal densities","volume":"81","author":"Tierney","year":"1986","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023071211302927300_qkad016-B33","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1111\/1467-9868.00374","article-title":"Thin plate regression splines","volume":"65","author":"Wood","year":"2003","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"515","key":"2023071211302927300_qkad016-B34","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1080\/01621459.2015.1086353","article-title":"Bayesian inference for dynamic treatment regimes: Mobility, equity, and efficiency in student tracking","volume":"111","author":"Xu","year":"2016","journal-title":"Journal of the American Statistical Association"},{"issue":"497","key":"2023071211302927300_qkad016-B35","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1080\/01621459.2011.643747","article-title":"Bayesian inference for dynamic treatment regimes: Mobility, equity, and efficiency in student tracking","volume":"107","author":"Zajonc","year":"2012","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2023071211302927300_qkad016-B36","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1093\/biomet\/ast014","article-title":"Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions","volume":"100","author":"Zhang","year":"2013","journal-title":"Biometrika"},{"issue":"4","key":"2023071211302927300_qkad016-B37","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1111\/j.1541-0420.2012.01763.x","article-title":"A robust method for estimating optimal treatment regimes","volume":"68","author":"Zhang","year":"2012","journal-title":"Biometrics"},{"issue":"26","key":"2023071211302927300_qkad016-B38","doi-asserted-by":"crossref","first-page":"3294","DOI":"10.1002\/sim.3720","article-title":"Reinforcement learning design for cancer clinical trials","volume":"28","author":"Zhao","year":"2009","journal-title":"Statistics in Medicine"},{"issue":"510","key":"2023071211302927300_qkad016-B39","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1080\/01621459.2014.937488","article-title":"New statistical learning methods for estimating optimal dynamic treatment regimes","volume":"110","author":"Zhao","year":"2015","journal-title":"Journal of the American Statistical Association"},{"issue":"499","key":"2023071211302927300_qkad016-B40","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1080\/01621459.2012.695674","article-title":"Estimating individualized treatment rules using outcome weighted learning","volume":"107","author":"Zhao","year":"2012","journal-title":"Journal of the American Statistical Association"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/3\/551\/50859755\/qkad016.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/3\/551\/50859755\/qkad016.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T11:32:28Z","timestamp":1689161548000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/3\/551\/7092905"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,29]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3,29]]},"published-print":{"date-parts":[[2023,7,12]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkad016","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,7]]},"published":{"date-parts":[[2023,3,29]]}}}