{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:14:51Z","timestamp":1764688491407,"version":"3.46.0"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T00:00:00Z","timestamp":1759881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"National Institute of Health","award":["T32AI007358","K01ES032458","R37AI131771","P30AI110527"],"award-info":[{"award-number":["T32AI007358","K01ES032458","R37AI131771","P30AI110527"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Exposure measurement error is a ubiquitous but often overlooked challenge in causal inference with observational data. Existing methods accounting for exposure measurement error largely rely on restrictive parametric assumptions, while emerging data-adaptive estimation approaches allow for less restrictive assumptions but at the cost of flexibility, as they are typically tailored toward rigidly defined statistical quantities. There remains a critical need for assumption-lean estimation methods that are both flexible and possess desirable theoretical properties across a variety of study designs. In this paper, we introduce a general framework for estimation of causal quantities in the presence of exposure measurement error, adapted from the method of control variates. Our method can be implemented in various two-phase sampling study designs, where one obtains gold-standard exposure measurements for a small subset of the full study sample, called the validation data. The control variates framework leverages both the error-prone and error-free exposure measurements by augmenting an initial consistent estimator from the validation data with a variance reduction term formed from the full data. We show that our method inherits double-robustness properties under standard causal assumptions. Simulation studies show that our approach performs favorably compared to leading methods under various two-phase sampling schemes. We illustrate our method with observational electronic health record data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.<\/jats:p>","DOI":"10.1093\/biomtc\/ujaf151","type":"journal-article","created":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T12:54:49Z","timestamp":1761656089000},"source":"Crossref","is-referenced-by-count":0,"title":["Flexible and efficient estimation of causal effects with error-prone exposures: a control variates approach for measurement error"],"prefix":"10.1093","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1451-9335","authenticated-orcid":false,"given":"Keith","family":"Barnatchez","sequence":"first","affiliation":[{"name":"Harvard T.H. Chan School of Public Health Department of Biostatistics, , Boston, MA 02115 ,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9895-1477","authenticated-orcid":false,"given":"Rachel","family":"Nethery","sequence":"additional","affiliation":[{"name":"Harvard T.H. Chan School of Public Health Department of Biostatistics, , Boston, MA 02115 ,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bryan E","family":"Shepherd","sequence":"additional","affiliation":[{"name":"Vanderbilt University Medical Center Department of Biostatistics, , Nashville, TN 37232 ,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8783-5961","authenticated-orcid":false,"given":"Giovanni","family":"Parmigiani","sequence":"additional","affiliation":[{"name":"Harvard T.H. Chan School of Public Health Department of Biostatistics, , Boston, MA 02115 ,","place":["United States"]},{"name":"Dana-Farber Cancer Institute Department of Data Science, , Boston, MA 02115 ,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2490-6272","authenticated-orcid":false,"given":"Kevin P","family":"Josey","sequence":"additional","affiliation":[{"name":"Colorado School of Public Health Department of Biostatistics and Informatics, , Aurora, CO 80045 ,","place":["United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,12,2]]},"reference":[{"key":"2025120210033149900_bib1","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1177\/0962280220988574","article-title":"Calibrating validation samples when accounting for measurement error in intervention studies","volume":"30","author":"Ackerman","year":"2021","journal-title":"Statistical Methods in Medical Research"},{"key":"2025120210033149900_bib2","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1111\/rssa.12689","article-title":"Two-phase sampling designs for data validation in settings with covariate measurement error and continuous outcome","volume":"184","author":"Amorim","year":"2021","journal-title":"Journal of the Royal Statistical Society Series A: Statistics in Society"},{"key":"2025120210033149900_bib3","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1093\/biostatistics\/kxx014","article-title":"Propensity scores with misclassified treatment assignment: a likelihood-based adjustment","volume":"18","author":"Braun","year":"2017","journal-title":"Biostatistics"},{"key":"2025120210033149900_bib4","first-page":"457","article-title":"Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis","volume":"48","author":"Breslow","year":"1999","journal-title":"Journal of the Royal Statistical Society: Series C (Applied Statistics)"},{"key":"2025120210033149900_bib5","doi-asserted-by":"crossref","DOI":"10.1201\/9781420010138","volume-title":"Measurement error in nonlinear models: a modern perspective","author":"Carroll","year":"2006"},{"key":"2025120210033149900_bib6","first-page":"685","article-title":"Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals","volume-title":"Biometrics","author":"Dahabreh","year":"2019"},{"key":"2025120210033149900_bib7","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1214\/20-AOAS1343","article-title":"Accounting for dependent errors in predictors and time-to-event outcomes using electronic health records, validation samples, and multiple imputation","volume":"14","author":"Giganti","year":"2020","journal-title":"The Annals of Applied Statistics"},{"key":"2025120210033149900_bib8","article-title":"Multi-source causal inference using control variates under outcome selection bias","author":"Guo","year":"2022","journal-title":"Transactions on Machine Learning Research"},{"key":"2025120210033149900_bib9","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1007\/s11336-016-9533-x","article-title":"Bayesian approach for addressing differential covariate measurement error in propensity score methods","volume":"82","author":"Hong","year":"2017","journal-title":"Psychometrika"},{"key":"2025120210033149900_bib10","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s13253-022-00508-z","article-title":"Estimating a causal exposure response function with a continuous error-prone exposure: a study of fine particulate matter and all-cause mortality","volume":"28","author":"Josey","year":"2023","journal-title":"Journal of Agricultural, Biological and Environmental Statistics"},{"key":"2025120210033149900_bib11","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1093\/jrsssb\/qkae099","article-title":"On the role of surrogates in the efficient estimation of treatment effects with limited outcome data","volume":"87","author":"Kallus","year":"2025","journal-title":"Journal of the Royal Statistical Society Series B: Statistical Methodology"},{"key":"2025120210033149900_bib12","doi-asserted-by":"crossref","first-page":"20190087","DOI":"10.1515\/ijb-2019-0087","article-title":"Efficient nonparametric causal inference with missing exposure information","volume":"16","author":"Kennedy","year":"2020","journal-title":"The International Journal of Biostatistics"},{"key":"2025120210033149900_bib13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1201\/9781003216223-10","article-title":"Semiparametric doubly robust targeted double machine learning: a review","author":"Kennedy","year":"2024","journal-title":"Handbook of Statistical Methods for Precision Medicine"},{"key":"2025120210033149900_bib14","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1201\/9781315101279-20","article-title":"Measurement error as a missing data problem","volume-title":"Handbook of Measurement Error Models","author":"Keogh","year":"2021"},{"key":"2025120210033149900_bib15","doi-asserted-by":"crossref","first-page":"371","DOI":"10.3102\/1076998616687084","article-title":"Multiple imputation under violated distributional assumptions: A systematic evaluation of the assumed robustness of predictive mean matching","volume":"42","author":"Kleinke","year":"2017","journal-title":"Journal of Educational and Behavioral Statistics"},{"key":"2025120210033149900_bib16","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1093\/aje\/kww068","article-title":"Correcting for measurement error in time-varying covariates in marginal structural models","volume":"184","author":"Kyle","year":"2016","journal-title":"American Journal of Epidemiology"},{"key":"2025120210033149900_bib17","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/07350015.1988.10509663","article-title":"Missing-data adjustments in large surveys","volume":"6","author":"Little","year":"1988","journal-title":"Journal of Business and Economic Statistics"},{"key":"2025120210033149900_bib18","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1080\/01621459.1938.10503378","article-title":"Contribution to the theory of sampling human populations","volume":"33","author":"Neyman","year":"1938","journal-title":"Journal of the American Statistical Association"},{"key":"2025120210033149900_bib19","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/sim.8793","article-title":"Raking and regression calibration: Methods to address bias from correlated covariate and time-to-event error","volume":"40","author":"Oh","year":"2021","journal-title":"Statistics in Medicine"},{"key":"2025120210033149900_bib20","doi-asserted-by":"crossref","first-page":"0000102202155746791217","DOI":"10.2202\/1557-4679.1217","article-title":"A targeted maximum likelihood estimator for two-stage designs","volume":"7","author":"Rose","year":"2011","journal-title":"The International Journal of Biostatistics"},{"key":"2025120210033149900_bib21","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1037\/h0037350","article-title":"Estimating causal effects of treatments in randomized and nonrandomized studies","volume":"66","author":"Rubin","year":"1974","journal-title":"Journal of Educational Psychology"},{"key":"2025120210033149900_bib22","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1287\/opre.33.3.661","article-title":"Efficiency of multivariate control variates in Monte Carlo simulation","volume":"33","author":"Rubinstein","year":"1985","journal-title":"Operations Research"},{"key":"2025120210033149900_bib23","volume-title":"Semiparametric Theory and Missing Data","author":"Tsiatis","year":"2006"},{"key":"2025120210033149900_bib24","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1201\/9781315101279-21","article-title":"Measurement error in causal inference","volume-title":"Handbook of Measurement Error Models","author":"Valeri","year":"2021"},{"key":"2025120210033149900_bib25","first-page":"1","article-title":"mice: Multivariate imputation by chained equations in R","volume":"45","author":"Van\u00a0Buuren","year":"2011","journal-title":"Journal of Statistical Software"},{"key":"2025120210033149900_bib26","first-page":"1","article-title":"Super learner","volume":"6","author":"Van\u00a0der\u00a0Laan","year":"2007","journal-title":"Statistical Applications in Genetics and Molecular Biology"},{"key":"2025120210033149900_bib27","volume-title":"Asymptotic statistics","author":"Van\u00a0der\u00a0Vaart","year":"2000"},{"key":"2025120210033149900_bib28","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1201\/9781315101279-3","article-title":"Identifiability in measurement error models","volume-title":"Handbook of Measurement Error Models","author":"Wang","year":"2021"},{"key":"2025120210033149900_bib29","doi-asserted-by":"crossref","first-page":"1824","DOI":"10.1177\/0962280215588771","article-title":"An imputation-based solution to using mismeasured covariates in propensity score analysis","volume":"26","author":"Webb-Vargas","year":"2017","journal-title":"Statistical Methods in Medical Research"},{"key":"2025120210033149900_bib30","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1214\/18-AOAS1206","article-title":"Causal inference in the context of an error prone exposure: air pollution and mortality","volume":"13","author":"Wu","year":"2019","journal-title":"The Annals of Applied Statistics"},{"key":"2025120210033149900_bib31","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1080\/01621459.2019.1609973","article-title":"Combining multiple observational data sources to estimate causal effects","volume":"115","author":"Yang","year":"2019","journal-title":"Journal of the American Statistical Association"}],"container-title":["Biometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/81\/4\/ujaf151\/65672275\/ujaf151.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/81\/4\/ujaf151\/65672275\/ujaf151.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:03:40Z","timestamp":1764687820000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biometrics\/article\/doi\/10.1093\/biomtc\/ujaf151\/8362787"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,8]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,10,8]]}},"URL":"https:\/\/doi.org\/10.1093\/biomtc\/ujaf151","relation":{},"ISSN":["0006-341X","1541-0420"],"issn-type":[{"value":"0006-341X","type":"print"},{"value":"1541-0420","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,12]]},"published":{"date-parts":[[2025,10,8]]},"article-number":"ujaf151"}}