{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T06:37:28Z","timestamp":1791441448725,"version":"4.3.3"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T00:00:00Z","timestamp":1692230400000},"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":[[2024,2,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The model-X conditional randomisation test (CRT) is a flexible and powerful testing procedure for testing the hypothesis X\u2aebY\u2223Z. However, it requires perfect knowledge of X\u2223Z and may lose its validity when there is an error in modelling X\u2223Z. This problem is even more severe when Z is of high dimensionality. In response to this, we propose the Maxway CRT, which learns the distribution of Y\u2223Z and uses it to calibrate the resampling distribution of X to gain robustness to the error in modelling X. We prove that the type-I error inflation of the Maxway CRT can be controlled by the learning error for a low-dimensional adjusting model plus the product of learning errors for X\u2223Z and Y\u2223Z, interpreted as an \u2018almost doubly robust\u2019 property. Based on this, we develop implementing algorithms of the Maxway CRT in practical scenarios including (surrogate-assisted) semi-supervised learning (SA-SSL) and transfer learning (TL). Through simulations, we demonstrate that the Maxway CRT achieves significantly better type-I error control than existing model-X inference approaches while preserving similar powers. Finally, we apply our methodology to two real examples of SA-SSL and TL.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad081","type":"journal-article","created":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T16:24:27Z","timestamp":1692289467000},"page":"1441-1470","source":"Crossref","is-referenced-by-count":1,"title":["Maxway CRT: improving the robustness of the model-X inference"],"prefix":"10.1093","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6272-4798","authenticated-orcid":false,"given":"Shuangning","family":"Li","sequence":"first","affiliation":[{"name":"Department of Statistics, Harvard University , Cambridge , United States"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Molei","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Columbia Mailman School of Public Health , New York , United States"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,8,17]]},"reference":[{"issue":"6","key":"2024020300382824900_qkad081-B1","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/S0002-8703(99)70080-3","article-title":"Clinical predictors of heart failure in patients with first acute myocardial infarction","volume":"138","author":"Ali","year":"1999","journal-title":"American Heart Journal"},{"issue":"3","key":"2024020300382824900_qkad081-B2","doi-asserted-by":"crossref","first-page":"1409","DOI":"10.1214\/19-AOS1852","article-title":"Robust inference with knockoffs","volume":"48","author":"Barber","year":"2020","journal-title":"The Annals of Statistics"},{"issue":"39","key":"2024020300382824900_qkad081-B3","doi-asserted-by":"crossref","first-page":"24117","DOI":"10.1073\/pnas.2007743117","article-title":"Causal inference in genetic trio studies","volume":"117","author":"Bates","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"2024020300382824900_qkad081-B4","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1093\/restud\/rdt044","article-title":"Inference on treatment effects after selection among high-dimensional controls","volume":"81","author":"Belloni","year":"2014","journal-title":"The Review of Economic Studies"},{"issue":"1","key":"2024020300382824900_qkad081-B5","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/rssb.12340","article-title":"The conditional permutation test for independence while controlling for confounders","volume":"82","author":"Berrett","year":"2020","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"2024020300382824900_qkad081-B6","author":"Cai","year":"2022"},{"issue":"3","key":"2024020300382824900_qkad081-B7","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1111\/rssb.12265","article-title":"Panning for gold: Model-X knockoffs for high dimensional controlled variable selection","volume":"80","author":"Cand\u00e8s","year":"2018","journal-title":"Journal of the Royal Statistical Society: Series B"},{"issue":"7911","key":"2024020300382824900_qkad081-B8","doi-asserted-by":"crossref","first-page":"f2610","DOI":"10.1136\/bmj.f2610","article-title":"Risk of incident diabetes among patients treated with statins: Population based study","volume":"346","author":"Carter","year":"2013","journal-title":"British Medical Journal"},{"issue":"9","key":"2024020300382824900_qkad081-B9","doi-asserted-by":"crossref","first-page":"961","DOI":"10.2337\/diacare.17.9.961","article-title":"Obesity, fat distribution, and weight gain as risk factors for clinical diabetes in men","volume":"17","author":"Chan","year":"1994","journal-title":"Diabetes Care"},{"issue":"1","key":"2024020300382824900_qkad081-B10","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":"The Econometrics Journal"},{"issue":"1","key":"2024020300382824900_qkad081-B11","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1093\/ectj\/utab022","article-title":"Regularized orthogonal machine learning for nonlinear semiparametric models","volume":"25","author":"Denis","year":"2021","journal-title":"The Econometrics Journal"},{"key":"2024020300382824900_qkad081-B12","author":"Dukes","year":"2021"},{"issue":"2","key":"2024020300382824900_qkad081-B13","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.pcad.2018.07.003","article-title":"An overview and update on obesity and the obesity paradox in cardiovascular diseases","volume":"61","author":"Elagizi","year":"2018","journal-title":"Progress in Cardiovascular Diseases"},{"key":"2024020300382824900_qkad081-B14","author":"Gu","year":"2022"},{"key":"2024020300382824900_qkad081-B15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/01621459.2023.2233162","article-title":"Assessing the most vulnerable subgroup to type II diabetes associated with statin usage: Evidence from electronic health record data","author":"Guo","year":"2023","journal-title":"Journal of the American Statistical Association"},{"key":"2024020300382824900_qkad081-B16","doi-asserted-by":"crossref","first-page":"S276","DOI":"10.2337\/dcS13-2023","article-title":"Obesity paradox does exist","volume":"36","author":"Hainer","year":"2013","journal-title":"Diabetes Care"},{"issue":"1","key":"2024020300382824900_qkad081-B17","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1111\/biom.12971","article-title":"Semi-supervised validation of multiple surrogate outcomes with application to electronic medical records phenotyping","volume":"75","author":"Hong","year":"2019","journal-title":"Biometrics"},{"key":"2024020300382824900_qkad081-B18","author":"Hou","year":"2021"},{"issue":"5","key":"2024020300382824900_qkad081-B19","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.1214\/19-AOS1920","article-title":"Relaxing the assumptions of knockoffs by conditioning","volume":"48","author":"Huang","year":"2020","journal-title":"The Annals of Statistics"},{"issue":"2","key":"2024020300382824900_qkad081-B20","doi-asserted-by":"crossref","first-page":"6348","DOI":"10.1214\/22-EJS2085","article-title":"On the power of conditional independence testing under model-X","volume":"16","author":"Katsevich","year":"2022","journal-title":"Electronic Journal of Statistics"},{"issue":"5","key":"2024020300382824900_qkad081-B21","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1056\/NEJMoa020245","article-title":"Obesity and the risk of heart failure","volume":"347","author":"Kenchaiah","year":"2002","journal-title":"New England Journal of Medicine"},{"issue":"1","key":"2024020300382824900_qkad081-B22","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1111\/rssb.12479","article-title":"Transfer learning for high-dimensional linear regression: Prediction, estimation and minimax optimality","volume":"84","author":"Li","year":"2022","journal-title":"Journal of the Royal Statistical Society Series B: Statistical Methodology"},{"key":"2024020300382824900_qkad081-B23","first-page":"1","article-title":"Transfer learning in genome-wide association studies with knockoffs","author":"Li","year":"2022","journal-title":"Sankhya B"},{"key":"2024020300382824900_qkad081-B24","author":"Liu","year":"2020"},{"issue":"126","key":"2024020300382824900_qkad081-B25","first-page":"1","article-title":"Integrative high dimensional multiple testing with heterogeneity under data sharing constraints","volume":"22","author":"Liu","year":"2021","journal-title":"Journal of Machine Learning Research"},{"issue":"3","key":"2024020300382824900_qkad081-B26","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1093\/ectj\/utab019","article-title":"Double\/debiased machine learning for logistic partially linear model","volume":"24","author":"Liu","year":"2021","journal-title":"The Econometrics Journal"},{"issue":"1","key":"2024020300382824900_qkad081-B27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2261-14-85","article-title":"Statins and the risk of type 2 diabetes mellitus: Cohort study using the UK clinical practice pesearch datalink","volume":"14","author":"Macedo","year":"2014","journal-title":"BMC Cardiovascular Disorders"},{"issue":"11","key":"2024020300382824900_qkad081-B28","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1007\/s11606-015-3335-1","article-title":"Statins and new-onset diabetes mellitus and diabetic complications: A retrospective cohort study of US healthy adults","volume":"30","author":"Mansi","year":"2015","journal-title":"Journal of General Internal Medicine"},{"issue":"1","key":"2024020300382824900_qkad081-B29","first-page":"2976","article-title":"L1-regularized least squares for support recovery of high dimensional single index models with Gaussian designs","volume":"17","author":"Neykov","year":"2016","journal-title":"The Journal of Machine Learning Research"},{"issue":"1","key":"2024020300382824900_qkad081-B30","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1056\/NEJMoa042000","article-title":"Statin therapy, LDL cholesterol, C-reactive protein, and coronary artery disease","volume":"352","author":"Nissen","year":"2005","journal-title":"New England Journal of Medicine"},{"key":"2024020300382824900_qkad081-B31","author":"Niu","year":"2022"},{"key":"2024020300382824900_qkad081-B32","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ahj.2019.09.016","article-title":"Association of obesity with cardiovascular outcomes in patients with type 2 diabetes and cardiovascular disease: Insights from TECOS","volume":"219","author":"Pagidipati","year":"2020","journal-title":"American Heart Journal"},{"issue":"4","key":"2024020300382824900_qkad081-B33","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1002\/sim.4780080407","article-title":"Surrogate endpoints in clinical trials: Definition and operational criteria","volume":"8","author":"Prentice","year":"1989","journal-title":"Statistics in Medicine"},{"issue":"3","key":"2024020300382824900_qkad081-B34","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1152\/physrev.1995.75.3.473","article-title":"Pathophysiology of insulin resistance in human disease","volume":"75","author":"Reaven","year":"1995","journal-title":"Physiological Reviews"},{"issue":"1","key":"2024020300382824900_qkad081-B35","first-page":"1","article-title":"Multi-resolution localization of causal variants across the genome","volume":"11","author":"Sesia","year":"2020","journal-title":"Nature Communications"},{"key":"2024020300382824900_qkad081-B36","author":"Sudarshan","year":"2021"},{"issue":"4","key":"2024020300382824900_qkad081-B37","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1093\/biomet\/ass043","article-title":"Scaled sparse linear regression","volume":"99","author":"Sun","year":"2012","journal-title":"Biometrika"},{"issue":"9822","key":"2024020300382824900_qkad081-B38","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1016\/S0140-6736(12)60110-X","article-title":"The interleukin-6 receptor as a target for prevention of coronary heart disease: A mendelian randomisation analysis","volume":"379","author":"Interleukin-6 Receptor Mendelian Randomisation Analysis (IL6R MR) Consortium","year":"2012","journal-title":"The Lancet"},{"issue":"9965","key":"2024020300382824900_qkad081-B39","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0140-6736(14)61183-1","article-title":"HMG-coenzyme a reductase inhibition, type 2 diabetes, and bodyweight: Evidence from genetic analysis and randomised trials","volume":"385","author":"Swerdlow","year":"2015","journal-title":"The Lancet"},{"key":"2024020300382824900_qkad081-B40","author":"Tansey","year":"2018"},{"key":"2024020300382824900_qkad081-B41","first-page":"1","article-title":"Transfer learning under high-dimensional generalized linear models","author":"Tian","year":"2022","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2024020300382824900_qkad081-B42","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1111\/biom.12071","article-title":"Surrogate measures and consistent surrogates","volume":"69","author":"VanderWeele","year":"2013","journal-title":"Biometrics"},{"issue":"3","key":"2024020300382824900_qkad081-B43","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1093\/biomet\/asab052","article-title":"A high-dimensional power analysis of the conditional randomization test and knockoffs","volume":"109","author":"Wang","year":"2022","journal-title":"Biometrika"},{"issue":"2","key":"2024020300382824900_qkad081-B44","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jacc.2012.09.042","article-title":"Cardiovascular event reduction versus new-onset diabetes during atorvastatin therapy: Effect of baseline risk factors for diabetes","volume":"61","author":"Waters","year":"2013","journal-title":"Journal of the American College of Cardiology"},{"issue":"10","key":"2024020300382824900_qkad081-B45","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1016\/j.jacc.2015.12.060","article-title":"Metabolomic profiling of statin use and genetic inhibition of HMG-CoA reductase","volume":"67","author":"W\u00fcrtz","year":"2016","journal-title":"Journal of the American College of Cardiology"},{"issue":"1","key":"2024020300382824900_qkad081-B46","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1093\/jamia\/ocz170","article-title":"A maximum likelihood approach to electronic health record phenotyping using positive and unlabeled patients","volume":"27","author":"Zhang","year":"2020","journal-title":"Journal of the American Medical Informatics Association"},{"issue":"83","key":"2024020300382824900_qkad081-B47","first-page":"1","article-title":"Prior adaptive semi-supervised learning with application to EHR phenotyping","volume":"23","author":"Zhang","year":"2022","journal-title":"Journal of Machine Learning Research"}],"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\/5\/1441\/56555162\/qkad081.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/5\/1441\/56555162\/qkad081.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T08:04:12Z","timestamp":1729843452000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/5\/1441\/7243739"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,17]]},"references-count":47,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,8,17]]},"published-print":{"date-parts":[[2024,2,2]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkad081","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,11]]},"published":{"date-parts":[[2023,8,17]]}}}