{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:34:07Z","timestamp":1770755647702,"version":"3.50.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01LM013352"],"award-info":[{"award-number":["R01LM013352"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["T32CA009337"],"award-info":[{"award-number":["T32CA009337"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["5P30CA077598-25"],"award-info":[{"award-number":["5P30CA077598-25"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Subgroup analyses of randomized controlled trials (RCTs) constitute an important component of the drug development process in precision medicine. In particular, subgroup analyses of early-stage trials often influence the design and eligibility criteria of subsequent confirmatory trials and ultimately influence which subpopulations will receive the treatment after regulatory approval. However, subgroup analyses are often complicated by small sample sizes, which leads to substantial uncertainty about subgroup-specific treatment effects. We explore the use of external control (EC) data to augment RCT subgroup analyses. We define and discuss harmonized estimators of subpopulation-specific treatment effects that leverage EC data. Our approach can be used to modify any subgroup-specific treatment effect estimates that are obtained by combining RCT and EC data, such as linear regression. We alter these subgroup-specific estimates to make them coherent with a robust estimate of the average effect in the randomized population based only on RCT data. The weighted average of the resulting subgroup-specific harmonized estimates matches the RCT-only estimate of the overall effect in the randomized population. We discuss the proposed harmonized estimators through analytic results and simulations, and investigate standard performance metrics. The method is illustrated with a case study in oncology.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf045","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T10:25:01Z","timestamp":1753352701000},"page":"143-170","source":"Crossref","is-referenced-by-count":0,"title":["Harmonized estimation of subgroup-specific treatment effects in randomized trials: the use of external control data"],"prefix":"10.1093","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3144-7919","authenticated-orcid":false,"given":"Daniel","family":"Schwartz","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA ,","place":["USA"]},{"name":"Department of Data Science, Dana-Farber Cancer Institute , Boston, MA ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riddhiman","family":"Saha","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2229-9560","authenticated-orcid":false,"given":"Steffen","family":"Ventz","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, School of Public Health, University of Minnesota , Minneapolis, MN ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorenzo","family":"Trippa","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA ,","place":["USA"]},{"name":"Department of Data Science, Dana-Farber Cancer Institute , Boston, MA ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"issue":"7","key":"2026021010563248900_qkaf045-B1","doi-asserted-by":"publisher","first-page":"e2200606","DOI":"10.1200\/PO.22.00606","article-title":"Validation of predictive analyses for interim decisions in clinical trials","volume":"7","author":"Avalos-Pacheco","year":"2023","journal-title":"JCO Precision Oncology"},{"issue":"1","key":"2026021010563248900_qkaf045-B2","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1214\/09-BA404","article-title":"Modularization in Bayesian analysis, with emphasis on analysis of computer models","volume":"4","author":"Bayarri","year":"2009","journal-title":"Bayesian Analysis"},{"issue":"1","key":"2026021010563248900_qkaf045-B3","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1111\/j.2517-6161.1976.tb01569.x","article-title":"Matrix weighted averages and posterior bounds","volume":"38","author":"Chamberlain","year":"1976","journal-title":"Journal of the Royal Statistical Society: Series B (Methodological)"},{"issue":"6","key":"2026021010563248900_qkaf045-B4","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1093\/aje\/kwn164","article-title":"Constructing inverse probability weights for marginal structural models","volume":"168","author":"Cole","year":"2008","journal-title":"American Journal of Epidemiology"},{"issue":"9","key":"2026021010563248900_qkaf045-B5","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1001\/jama.2018.10136","article-title":"Real-world evidence and real-world data for evaluating drug safety and effectiveness","volume":"320","author":"Corrigan-Curay","year":"2018","journal-title":"JAMA"},{"issue":"Suppl 2","key":"2026021010563248900_qkaf045-B6","doi-asserted-by":"publisher","first-page":"102293","DOI":"10.1016\/j.ctrv.2021.102293","article-title":"The impact of radiological assessment schedules on progression-free survival in metastatic breast cancer: A systemic review and meta-analysis","volume":"100","author":"Dabush","year":"2021","journal-title":"Cancer Treatment Reviews"},{"issue":"5","key":"2026021010563248900_qkaf045-B7","doi-asserted-by":"publisher","first-page":"e746","DOI":"10.1634\/theoncologist.2019-0647","article-title":"Real-world evidence in oncology: Opportunities and limitations","volume":"25","author":"Di Maio","year":"2020","journal-title":"The Oncologist"},{"issue":"6","key":"2026021010563248900_qkaf045-B8","first-page":"515","article-title":"How to work with a subgroup analysis","volume":"52","author":"Dijkman","year":"2009","journal-title":"Canadian Journal of Surgery"},{"issue":"1","key":"2026021010563248900_qkaf045-B9","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1214\/ss\/1177013815","article-title":"Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy","volume":"1","author":"Efron","year":"1986","journal-title":"Statistical Science"},{"key":"2026021010563248900_qkaf045-B10","doi-asserted-by":"crossref","DOI":"10.1017\/9781139029834","volume-title":"Fundamentals of nonparametric Bayesian inference","author":"Ghosal","year":"2017","edition":"1st ed."},{"issue":"3","key":"2026021010563248900_qkaf045-B11","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1214\/19-BA1195","article-title":"Bayesian regression tree models for causal inference: Regularization, confounding, and heterogeneous effects (with discussion)","volume":"15","author":"Hahn","year":"2020","journal-title":"Bayesian Analysis"},{"issue":"3","key":"2026021010563248900_qkaf045-B12","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1177\/1740774513483934","article-title":"Adaptive adjustment of the randomization ratio using historical control data","volume":"10","author":"Hobbs","year":"2013","journal-title":"Clinical Trials"},{"issue":"3","key":"2026021010563248900_qkaf045-B13","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1214\/12-BA722","article-title":"Commensurate priors for incorporating historical information in clinical trials using general and generalized linear models","volume":"7","author":"Hobbs","year":"2012","journal-title":"Bayesian Analysis"},{"issue":"28","key":"2026021010563248900_qkaf045-B14","doi-asserted-by":"publisher","first-page":"3724","DOI":"10.1002\/sim.6728","article-title":"The power prior: Theory and applications","volume":"34","author":"Ibrahim","year":"2015","journal-title":"Statistics in Medicine"},{"key":"2026021010563248900_qkaf045-B15","doi-asserted-by":"publisher","author":"Jacob","DOI":"10.48550\/arXiv.1708.08719"},{"issue":"2","key":"2026021010563248900_qkaf045-B16","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1177\/1740774510396933","article-title":"Bayesian models for subgroup analysis in clinical trials","volume":"8","author":"Jones","year":"2011","journal-title":"Clinical Trials"},{"issue":"3","key":"2026021010563248900_qkaf045-B17","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1111\/rssc.12550","article-title":"Generalizing trial evidence to target populations in non-nested designs: Applications to AIDS clinical trials","volume":"71","author":"Li","year":"2022","journal-title":"Journal of the Royal Statistical Society: Series C, Applied Statistics"},{"issue":"5","key":"2026021010563248900_qkaf045-B18","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1177\/2168479018778282","article-title":"Minimizing patient burden through the use of historical subject-level data in innovative confirmatory clinical trials: Review of methods and opportunities","volume":"52","author":"Lim","year":"2018","journal-title":"Therapeutic Innovation & Regulatory Science"},{"issue":"2","key":"2026021010563248900_qkaf045-B19","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1002\/pst.1918","article-title":"Propensity-score-based priors for Bayesian augmented control design","volume":"18","author":"Lin","year":"2019","journal-title":"Pharmaceutical Statistics"},{"issue":"19","key":"2026021010563248900_qkaf045-B20","doi-asserted-by":"publisher","first-page":"2937","DOI":"10.1002\/sim.1903","article-title":"Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study","volume":"23","author":"Lunceford","year":"2004","journal-title":"Statistics in Medicine"},{"issue":"4","key":"2026021010563248900_qkaf045-B21","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1111\/biom.12677","article-title":"Bayesian population finding with biomarkers in a randomized clinical trial","volume":"73","author":"Morita","year":"2017","journal-title":"Biometrics"},{"issue":"4","key":"2026021010563248900_qkaf045-B22","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1001\/jamainternmed.2016.9138","article-title":"The challenges of generating evidence to support precision medicine","volume":"177","author":"Pletcher","year":"2017","journal-title":"JAMA Internal Medicine"},{"issue":"12","key":"2026021010563248900_qkaf045-B23","doi-asserted-by":"publisher","first-page":"2194","DOI":"10.1158\/1078-0432.CCR-22-3524","article-title":"Accessible data collections for improved decision making in neuro-oncology clinical trials","volume":"29","author":"Rahman","year":"2023","journal-title":"Clinical Cancer Research"},{"issue":"9-12","key":"2026021010563248900_qkaf045-B24","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1016\/0270-0255(86)90088-6","article-title":"A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect","volume":"7","author":"Robins","year":"1986","journal-title":"Mathematical Modelling"},{"issue":"4","key":"2026021010563248900_qkaf045-B25","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1111\/biom.v70.4","article-title":"Robust meta-analytic-predictive priors in clinical trials with historical control information: Robust meta-analytic-predictive priors","volume":"70","author":"Schmidli","year":"2014","journal-title":"Biometrics"},{"issue":"15","key":"2026021010563248900_qkaf045-B26","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.1002\/sim.7276","article-title":"Subgroup finding via Bayesian additive regression trees","volume":"36","author":"Sivaganesan","year":"2017","journal-title":"Statistics in Medicine"},{"issue":"7","key":"2026021010563248900_qkaf045-B27","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1093\/aje\/kwq472","article-title":"Implementation of G-computation on a simulated data set: Demonstration of a causal inference technique","volume":"173","author":"Snowden","year":"2011","journal-title":"American Journal of Epidemiology"},{"issue":"5","key":"2026021010563248900_qkaf045-B28","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/S1470-2045(09)70025-7","article-title":"Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial","volume":"10","author":"Stupp","year":"2009","journal-title":"The Lancet: Oncology"},{"issue":"10","key":"2026021010563248900_qkaf045-B29","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1056\/NEJMoa043330","article-title":"Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma","volume":"352","author":"Stupp","year":"2005","journal-title":"New England Journal of Medicine"},{"issue":"1","key":"2026021010563248900_qkaf045-B30","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1186\/1745-6215-14-166","article-title":"A reinvestigation of recruitment to randomised, controlled, multicenter trials: A review of trials funded by two UK funding agencies","volume":"14","author":"Sully","year":"2013","journal-title":"Trials"},{"issue":"mar15 1","key":"2026021010563248900_qkaf045-B31","doi-asserted-by":"publisher","first-page":"e1553","DOI":"10.1136\/bmj.e1553","article-title":"Credibility of claims of subgroup effects in randomised controlled trials: Systematic review","volume":"344","author":"Sun","year":"2012","journal-title":"BMJ"},{"issue":"3","key":"2026021010563248900_qkaf045-B32","doi-asserted-by":"publisher","first-page":"239","DOI":"10.3102\/1076998612441947","article-title":"Improving generalizations from experiments using propensity score subclassification: Assumptions, properties, and contexts","volume":"38","author":"Tipton","year":"2013","journal-title":"Journal of Educational and Behavioral Statistics"},{"issue":"6","key":"2026021010563248900_qkaf045-B33","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1200\/JCO.2016.68.2864","article-title":"Bayesian baskets: A novel design for biomarker-based clinical trials","volume":"35","author":"Trippa","year":"2017","journal-title":"Journal of Clinical Oncology: Official Journal of the American Society of Clinical Oncology"},{"issue":"36","key":"2026021010563248900_qkaf045-B34","doi-asserted-by":"publisher","first-page":"4274","DOI":"10.1200\/JCO.20.02151","article-title":"TBCRC 048: Phase II study of olaparib for metastatic breast cancer and mutations in homologous recombination-related genes","volume":"38","author":"Tung","year":"2020","journal-title":"Journal of Clinical Oncology"},{"issue":"2","key":"2026021010563248900_qkaf045-B35","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1093\/neuonc\/noab141","article-title":"The use of external control data for predictions and futility interim analyses in clinical trials","volume":"24","author":"Ventz","year":"2022","journal-title":"Neuro-Oncology"},{"issue":"16","key":"2026021010563248900_qkaf045-B36","doi-asserted-by":"publisher","first-page":"4993","DOI":"10.1158\/1078-0432.CCR-19-0820","article-title":"Design and evaluation of an external control arm using prior clinical trials and real-world data","volume":"25","author":"Ventz","year":"2019","journal-title":"Clinical Cancer Research"},{"issue":"1","key":"2026021010563248900_qkaf045-B37","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1002\/pst.1589","article-title":"Use of historical control data for assessing treatment effects in clinical trials","volume":"13","author":"Viele","year":"2014","journal-title":"Pharmaceutical Statistics"},{"issue":"21","key":"2026021010563248900_qkaf045-B38","doi-asserted-by":"publisher","first-page":"2189","DOI":"10.1056\/NEJMsr077003","article-title":"Statistics in medicine\u2014reporting of subgroup analyses in clinical trials","volume":"357","author":"Wang","year":"2007","journal-title":"New England Journal of Medicine"}],"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\/88\/1\/143\/63837948\/qkaf045.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/88\/1\/143\/63837948\/qkaf045.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T15:56:38Z","timestamp":1770738998000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/88\/1\/143\/8211632"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,24]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,7,24]]},"published-print":{"date-parts":[[2026,2,10]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkaf045","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,2]]},"published":{"date-parts":[[2025,7,24]]}}}