{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:46:46Z","timestamp":1792673206232,"version":"4.5.0"},"reference-count":27,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T00:00:00Z","timestamp":1792627200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T00:00:00Z","timestamp":1792627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Pharmaceutical Statistics"],"published-print":{"date-parts":[[2026,11]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    Evaluating treatment effect heterogeneity across patient subgroups is a fundamental aspect of clinical trial analysis. Yet, these analyses have inherent limitations due to small sample sizes and the substantial number of subgroups investigated. There is also a tendency to focus on extreme estimates, which may reflect random variation rather than true effects, potentially leading to spurious clinical conclusions. In recent years, statisticians in regulatory agencies and pharmaceutical companies have begun considering shrinkage methods grounded in Bayesian statistical theory. These methods incorporate priors on treatment effect heterogeneity, which operationally shrink raw subgroup treatment effect estimates towards the overall treatment effect. Various shrinkage estimators and priors have been proposed, yet it remains unclear which methods perform best. This work provides a unified presentation and software implementation for continuous, binary, count, and time\u2010to\u2010event endpoints in the\n                    <jats:styled-content>R<\/jats:styled-content>\n                    package\n                    <jats:styled-content>bonsaiforest2<\/jats:styled-content>\n                    . It also provides simulation comparisons of one\u2010way and global shrinkage methods for two distinct simulation set\u2010ups. One\u2010way models fit a separate shrinkage model for each subgrouping variable, whereas global models fit a model including all subgroup indicators at once. Both can derive standardized subgroup\u2010specific treatment effects. Across all simulation scenarios, shrinkage methods outperformed the standard subgroup estimator without shrinkage in terms of mean squared error. They were also more efficient in identifying a non\u2010efficacious subgroup. Global shrinkage models tended to have smaller mean squared error and less dependence on hyperprior parameters than one\u2010way models, but also exhibited slightly larger bias and worse frequentist coverage of associated credible intervals. For both models, hyperprior choices anchored in trial assumptions about the anticipated size of the overall treatment effect performed well. We conclude that some degree of shrinkage is preferable to none and advocate for the routine inclusion of shrunken estimates in clinical forest plots to facilitate more robust decision\u2010making.\n                  <\/jats:p>","DOI":"10.1002\/pst.70137","type":"journal-article","created":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:21:28Z","timestamp":1792671688000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unified Implementation and Comparison of Bayesian Shrinkage Methods for Treatment Effect Estimation in Subgroups"],"prefix":"10.1002","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4915-9015","authenticated-orcid":false,"given":"Marcel","family":"Wolbers","sequence":"first","affiliation":[{"name":"Clinical Statistics and Analytics, Bayer BCC AG  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0100-9378","authenticated-orcid":false,"given":"Miriam Pedrera","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Indivi AG  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1967-039X","authenticated-orcid":false,"given":"Alex","family":"Ocampo","sequence":"additional","affiliation":[{"name":"Data Science and Analytics, Roche  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0283-2065","authenticated-orcid":false,"given":"Isaac","family":"Gravestock","sequence":"additional","affiliation":[{"name":"Clinical Statistics and Analytics, Bayer BCC AG  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,22]]},"reference":[{"issue":"1","key":"e_1_2_11_2_1","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1002\/sim.7064","article-title":"Tutorial in Biostatistics: Data\u2010Driven Subgroup Identification and Analysis in Clinical Trials","volume":"36","author":"Lipkovich I.","year":"2017","journal-title":"Statistics in Medicine"},{"issue":"1","key":"e_1_2_11_3_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/cvm-1-1-025","article-title":"Debate: Subgroup Analyses in Clinical Trials: Fun to Look At\u2010But Don't Believe Them!","volume":"1","author":"Sleight P.","year":"2000","journal-title":"Trials"},{"issue":"32","key":"e_1_2_11_4_1","doi-asserted-by":"crossref","first-page":"E901","DOI":"10.1503\/cmaj.200077","article-title":"Development of the Instrument to Assess the Credibility of Effect Modification Analyses (ICEMAN) in Randomized Controlled Trials and Meta\u2010Analyses","volume":"192","author":"Schandelmaier S.","year":"2020","journal-title":"Canadian Medical Association Journal"},{"key":"e_1_2_11_5_1","unstructured":"EMA Biostatistics Working Party \u201cGuideline on the Investigation of Subgroups in Confirmatory Clinical Trials \u201d(2019) https:\/\/www.ema.europa.eu\/en\/documents\/scientific\u2010guideline\/guideline\u2010investigation\u2010subgroups\u2010confirmatory\u2010clinical\u2010trials_en.pdf."},{"issue":"3","key":"e_1_2_11_6_1","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1002\/bimj.201900297","article-title":"Making Apples From Oranges: Comparing Noncollapsible Effect Estimators and Their Standard Errors After Adjustment for Different Covariate Sets","volume":"63","author":"Daniel R.","year":"2021","journal-title":"Biometrical Journal"},{"issue":"2","key":"e_1_2_11_7_1","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1002\/bimj.202000202","article-title":"Correct and Logical Causal Inference for Binary and Time\u2010To\u2010Event Outcomes in Randomized Controlled Trials","volume":"64","author":"Liu Y.","year":"2022","journal-title":"Biometrical Journal"},{"issue":"2","key":"e_1_2_11_8_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1177\/1740774510396933","article-title":"Bayesian Models for Subgroup Analysis in Clinical Trials","volume":"8","author":"Jones H. 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D.","year":"2022","journal-title":"Journal of the American Statistical Association"}],"container-title":["Pharmaceutical Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pst.70137","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/pst.70137","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pst.70137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:21:33Z","timestamp":1792671693000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pst.70137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,22]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,11]]}},"alternative-id":["10.1002\/pst.70137"],"URL":"https:\/\/doi.org\/10.1002\/pst.70137","archive":["Portico"],"relation":{},"ISSN":["1539-1604","1539-1612"],"issn-type":[{"value":"1539-1604","type":"print"},{"value":"1539-1612","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,22]]},"assertion":[{"value":"2026-03-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-22","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70137"}}