{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T13:10:01Z","timestamp":1759065001574,"version":"3.44.0"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Cox regression is the default approach to evaluating the (relative) effect of two treatments on a survival endpoint. This standard framework has nonetheless been criticized for its canonical effect measure, the hazard ratio, having a subtle interpretation, thereby hindering policy-making. This in turn has prompted interest in other effects measures, such as the difference in restricted mean survival time, the net benefit and the win ratio, which have become increasingly popular. Developments in estimation and inference for the net benefit and win ratio proceed either under a semiparametric model, at the risk of bias due to model misspecification, or in a nonparametric model, but without the flexibility to adjust for covariates. In this paper, we overcome these challenges by introducing a scalar, model-free measure of conditional causal net benefit in terms of counterfactuals and developing a debiased estimator based on its efficient influence function. This estimator is root-$ n $ consistent and asymptotically model-free by flexibly enabling data-adaptive learning (e.g., machine learning) of the dependence of treatment, survival and censoring time on baseline covariates. By incorporating such covariates, the proposed estimators can improve the efficiency of randomized trial analyses, as well as correct for confounding and censoring bias in both randomized and observational studies. We also propose variations of the considered estimand (and estimator) that have a more favourable efficiency bound. The proposed method is illustrated by simulation studies and analysis of breast cancer data.<\/jats:p>","DOI":"10.1093\/biomet\/asaf051","type":"journal-article","created":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T14:14:16Z","timestamp":1752502456000},"source":"Crossref","is-referenced-by-count":0,"title":["Debiased learning of the causal net benefit with censored event time data"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9760-6791","authenticated-orcid":false,"given":"Torben","family":"Martinussen","sequence":"first","affiliation":[{"name":"Section of Biostatistics, Department of Public Health, University of Copenhagen , \u00d8ster Farimagsgade 5 opg. B , 1353 Copenhagen,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stijn","family":"Vansteelandt","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Computer Science and Statistics, Ghent University , Krijgslaan 281 (S9) , 9000 Ghent,","place":["Belgium"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"key":"2025092808414482400_asaf051-B1","doi-asserted-by":"crossref","first-page":"C1","DOI":"10.1111\/ectj.12097","article-title":"Double\/debiased machine learning for treatment and structural parameters","volume":"21","author":"Chernozhukov","year":"2018","journal-title":"Economet. J"},{"year":"2023","author":"Cui","key":"2025092808414482400_asaf051-B2"},{"key":"2025092808414482400_asaf051-B3","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1002\/bimj.201800255","article-title":"On the interpretation of the hazard ratio in Cox regression","volume":"62","author":"De Neve","year":"2020","journal-title":"Biomet. J"},{"key":"2025092808414482400_asaf051-B4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s10985-018-9428-5","article-title":"Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards","volume":"25","author":"D\u00edaz","year":"2019","journal-title":"Lifetime Data Anal"},{"key":"2025092808414482400_asaf051-B5","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1002\/sim.7799","article-title":"Causal estimands and confidence intervals associated with Wilcoxon--Mann--Whitney tests in randomized experiments","volume":"37","author":"Fay","year":"2018","journal-title":"Statist. Med"},{"key":"2025092808414482400_asaf051-B6","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00031305.2019.1575771","article-title":"On causal inferences for personalized medicine: How hidden causal assumptions led to erroneous causal claims about the D-value","volume":"74","author":"Greenland","year":"2020","journal-title":"Am. Statistician"},{"key":"2025092808414482400_asaf051-B7","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1097\/EDE.0b013e3181c1ea43","article-title":"The hazards of hazard ratios","volume":"21","author":"Hern\u00e1n","year":"2010","journal-title":"Epidemiology"},{"year":"2022","author":"Kennedy","key":"2025092808414482400_asaf051-B8"},{"key":"2025092808414482400_asaf051-B9","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1093\/biomet\/asn003","article-title":"Improving the efficiency of the log-rank test using auxiliary covariates","volume":"95","author":"Lu","year":"2008","journal-title":"Biometrika"},{"key":"2025092808414482400_asaf051-B10","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1111\/biom.13382","article-title":"A class of proportional win-fractions regression models for composite outcomes","volume":"77","author":"Mao","year":"2021","journal-title":"Biometrics"},{"key":"2025092808414482400_asaf051-B11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10985-013-9242-z","article-title":"On collapsibility and confounding bias in Cox and Aalen regression models","volume":"19","author":"Martinussen","year":"2013","journal-title":"Lifetime Data Anal"},{"key":"2025092808414482400_asaf051-B12","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1007\/s10985-020-09501-5","article-title":"Subtleties in the interpretation of hazard contrasts","volume":"26","author":"Martinussen","year":"2020","journal-title":"Lifetime Data Anal"},{"key":"2025092808414482400_asaf051-B13","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1177\/09622802211037067","article-title":"The asymptotic distribution of the net benefit estimator in presence of right-censoring","volume":"30","author":"Ozenne","year":"2021","journal-title":"Statist. Meth. Med. Res"},{"key":"2025092808414482400_asaf051-B14","first-page":"901","article-title":"The net chance of a longer survival as a patient-oriented measure of treatment benefit in randomized clinical trials","volume":"2","author":"P\u00e9ron","year":"2016","journal-title":"J. Am. Med. Assoc. Oncol."},{"key":"2025092808414482400_asaf051-B15","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1093\/eurheartj\/ehr352","article-title":"The win ratio: A new approach to the analysis of composite endpoints in clinical trials based on clinical priorities","volume":"33","author":"Pocock","year":"2012","journal-title":"Eur. Heart J"},{"key":"2025092808414482400_asaf051-B16","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1214\/21-STS830","article-title":"Intention-to-treat comparisons in randomized trials","volume":"37","author":"Prentice","year":"2022","journal-title":"Statist. Sci"},{"volume-title":"R: A Language and Environment for Statistical Computing","year":"2025","author":"R Development Core Team","key":"2025092808414482400_asaf051-B17"},{"key":"2025092808414482400_asaf051-B18","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1093\/jnci\/djx179","article-title":"Understanding and communicating measures of treatment effect on survival: Can we do better?","volume":"110","author":"Saad","year":"2018","journal-title":"J. Nat. Cancer Inst"},{"key":"2025092808414482400_asaf051-B19","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1200\/JCO.1994.12.10.2086","article-title":"Randomized $2 \\times 2$ trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. German breast cancer study group","volume":"12","author":"Schumacher","year":"1994","journal-title":"J. Clin. Oncol"},{"key":"2025092808414482400_asaf051-B20","doi-asserted-by":"crossref","first-page":"3944","DOI":"10.1002\/sim.2587","article-title":"Comment on \u2018Probabilistic index: An intuitive non-parametric approach to measuring the size of the treatment effects\u2019 by L. Acion, J. J. Peterson, S. Temple and S. Arndt, Statistics in Medicine 2006; 25 (4): 591\u2013602","volume":"25","author":"Senn","year":"2006","journal-title":"Statist. Med"},{"key":"2025092808414482400_asaf051-B21","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1080\/10543406.2022.2089156","article-title":"The win odds: Statistical inference and regression","volume":"33","author":"Song","year":"2023","journal-title":"J. Biopharm. Statist"},{"key":"2025092808414482400_asaf051-B22","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1001\/jama.2020.1267","article-title":"Why test for proportional hazards?","volume":"323","author":"Stensrud","year":"2020","journal-title":"J. Am. Med. Assoc"},{"key":"2025092808414482400_asaf051-B23","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1093\/biomet\/73.2.363","article-title":"Misspecified proportional hazard models","volume":"73","author":"Struthers","year":"1986","journal-title":"Biometrika"},{"volume-title":"Asymptotic Statistics","year":"2000","author":"van der Vaart","key":"2025092808414482400_asaf051-B24"},{"key":"2025092808414482400_asaf051-B25","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1080\/01621459.2022.2126362","article-title":"Assumption-lean Cox regression","volume":"119","author":"Vansteelandt","year":"2024","journal-title":"J. Am. Statist. Assoc"},{"key":"2025092808414482400_asaf051-B26","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1080\/10543406.2023.2275759","article-title":"Adjusted win ratio using the inverse probability of treatment weighting","volume":"35","author":"Wang","year":"2023","journal-title":"J. Biopharm. Statist"},{"key":"2025092808414482400_asaf051-B27","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1080\/01621459.2023.2205060","article-title":"Inference for treatment-specific survival curves using machine learning","volume":"119","author":"Westling","year":"2024","journal-title":"J. Am. Statist. Assoc"},{"key":"2025092808414482400_asaf051-B28","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1111\/biom.12384","article-title":"On the restricted mean survival time curve in survival analysis","volume":"72","author":"Zhao","year":"2016","journal-title":"Biometrics"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaf051\/63778951\/asaf051.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/112\/3\/asaf051\/63778951\/asaf051.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/112\/3\/asaf051\/63778951\/asaf051.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:41:57Z","timestamp":1759063317000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/doi\/10.1093\/biomet\/asaf051\/8203474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,7,16]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaf051","relation":{},"ISSN":["1464-3510"],"issn-type":[{"type":"electronic","value":"1464-3510"}],"subject":[],"published-other":{"date-parts":[[2025]]},"published":{"date-parts":[[2025]]},"article-number":"asaf051"}}