{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T12:06:19Z","timestamp":1779192379932,"version":"3.51.4"},"reference-count":62,"publisher":"Wiley","issue":"8-9","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":7,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100012774","name":"Innovationsfonden","doi-asserted-by":"publisher","award":["2052\u201000044B"],"award-info":[{"award-number":["2052\u201000044B"]}],"id":[{"id":"10.13039\/100012774","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In randomized clinical trials (RCTs), the accurate estimation of marginal treatment effects is crucial for determining the efficacy of interventions. Enhancing the statistical power of these analyses is a key objective for statisticians. The increasing availability of historical data from registries, prior trials, and health records presents an opportunity to improve trial efficiency. However, many methods for historical borrowing compromise strict type I error rate control. Building on the work by Schuler et al. on prognostic score adjustment for linear models, this paper extends the methodology to the plug\u2010in analysis proposed by Rosenblum and van der Laan using generalized linear models (GLMs) to further enhance the efficiency of RCT analyses without introducing bias. Specifically, we train a prognostic model on historical control data and incorporate the resulting prognostic scores as covariates in the plug\u2010in GLM analysis of the trial data. This approach leverages the predictive power of historical data to improve the precision of marginal treatment effect estimates. We demonstrate that this method achieves local semi\u2010parametric efficiency under the assumption of an additive treatment effect on the link scale. We expand the GLM plug\u2010in method to include Negative Binomial regression. Additionally, we provide a straightforward formula for conservatively estimating the asymptotic variance, facilitating power calculations that reflect these efficiency gains. Our simulation study supports the theory. Even without an additive treatment effect, we observe increased power or reduced standard error. While population shifts from historical to trial data may dilute benefits, they do not introduce bias. We demonstrate reductions in the estimated variance through an analysis of clinical trial data provided by Novo Nordisk A\/S.<\/jats:p>","DOI":"10.1002\/sim.70524","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T12:11:37Z","timestamp":1775650297000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Powering RCTs for Marginal Effects With GLMs Using Prognostic Score Adjustment"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0996-4363","authenticated-orcid":false,"given":"Emilie","family":"H\u00f8jbjerre\u2010Frandsen","sequence":"first","affiliation":[{"name":"Biostatistics Methods Novo Nordisk A\/S  S\u00f8borg Denmark"},{"name":"Department of Mathematical Sciences Aalborg University  Aalborg \u00d8st Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark J.","family":"van der Laan","sequence":"additional","affiliation":[{"name":"Division of Biostatistics University of California Berkeley  Berkeley California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alejandro","family":"Schuler","sequence":"additional","affiliation":[{"name":"Division of Biostatistics University of California Berkeley  Berkeley California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"e_1_2_14_2_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmjopen\u20102016\u2010011666"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/82.4.669"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774518820060"},{"key":"e_1_2_14_5_1","doi-asserted-by":"publisher","DOI":"10.7326\/0003\u20104819\u2010133\u20106\u2010200009190\u201000014"},{"key":"e_1_2_14_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7023"},{"key":"e_1_2_14_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.70028"},{"key":"e_1_2_14_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3445"},{"key":"e_1_2_14_9_1","doi-asserted-by":"publisher","DOI":"10.2202\/1557\u20104679.1138"},{"key":"e_1_2_14_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3113"},{"key":"e_1_2_14_11_1","unstructured":"Center for Drug Evaluation and Research & Center for Biologics Evaluation and Research Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products \u2010 Guidance for Industry(2023) https:\/\/www.fda.gov\/media\/148910\/download."},{"key":"e_1_2_14_12_1","unstructured":"Committee for Medicinal Products for Human Use Guideline on Adjustment for Baseline Covariates in Clinical Trials(2015) https:\/\/www.ema.europa.eu\/en\/documents\/scientific\u2010guideline\/guideline\u2010adjustment\u2010baseline\u2010covariates\u2010clinical\u2010trials_en.pdf."},{"key":"e_1_2_14_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4301"},{"key":"e_1_2_14_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2009.06.002"},{"key":"e_1_2_14_15_1","doi-asserted-by":"publisher","DOI":"10.1186\/1745\u20106215\u201015\u2010139"},{"key":"e_1_2_14_16_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomtc\/ujad034"},{"key":"e_1_2_14_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2329"},{"key":"e_1_2_14_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0197-2456(93)90225-3"},{"key":"e_1_2_14_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2433396.2433413"},{"key":"e_1_2_14_20_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asn004"},{"key":"e_1_2_14_21_1","doi-asserted-by":"publisher","DOI":"10.1515\/ijb\u20102021\u20100072"},{"key":"e_1_2_14_22_1","unstructured":"R.Karlsson G.Wang J. 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