{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T17:50:08Z","timestamp":1792000208256,"version":"4.4.0"},"reference-count":69,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,9,24]],"date-time":"2020-09-24T00:00:00Z","timestamp":1600905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,5,15]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical applications, such as personalized medicine and optimal resource allocation. In this article we develop a general class of two-step algorithms for heterogeneous treatment effect estimation in observational studies. First, we estimate marginal effects and treatment propensities to form an objective function that isolates the causal component of the signal. Then, we optimize this data-adaptive objective function. The proposed approach has several advantages over existing methods. From a practical perspective, our method is flexible and easy to use: in both steps, any loss-minimization method can be employed, such as penalized regression, deep neural networks, or boosting; moreover, these methods can be fine-tuned by cross-validation. Meanwhile, in the case of penalized kernel regression, we show that our method has a quasi-oracle property. Even when the pilot estimates for marginal effects and treatment propensities are not particularly accurate, we achieve the same error bounds as an oracle with prior knowledge of these two nuisance components. We implement variants of our approach based on penalized regression, kernel ridge regression, and boosting in a variety of simulation set-ups, and observe promising performance relative to existing baselines.<\/jats:p>","DOI":"10.1093\/biomet\/asaa076","type":"journal-article","created":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T23:39:32Z","timestamp":1599694772000},"page":"299-319","source":"Crossref","is-referenced-by-count":483,"title":["Quasi-oracle estimation of heterogeneous treatment effects"],"prefix":"10.1093","volume":"108","author":[{"given":"X","family":"Nie","sequence":"first","affiliation":[{"name":"Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S","family":"Wager","sequence":"additional","affiliation":[{"name":"Stanford Graduate School of Business, 655 Knight Way, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,24]]},"reference":[{"key":"2021051519491947400_B1","first-page":"265","article-title":"TensorFlow: A system for large-scale machine learning","author":"Abadi,","year":"2016","journal-title":"Proc. 12th USENIX Sympos. Operating Systems Design and Implementation (OSDI\u201916)"},{"key":"2021051519491947400_B2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1093\/pan\/mpj001","article-title":"Comparing experimental and matching methods using a large-scale voter mobilization experiment","volume":"14","author":"Arceneaux,","year":"2006","journal-title":"Polit. Anal."},{"key":"2021051519491947400_B3","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1126\/science.aal4321","article-title":"Beyond prediction: Using big data for policy problems","volume":"355","author":"Athey,","year":"2017","journal-title":"Science"},{"key":"2021051519491947400_B4","doi-asserted-by":"crossref","first-page":"7353","DOI":"10.1073\/pnas.1510489113","article-title":"Recursive partitioning for heterogeneous causal effects","volume":"113","author":"Athey,","year":"2016","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2021051519491947400_B5","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1214\/18-AOS1709","article-title":"Generalized random forests","volume":"47","author":"Athey,","year":"2019","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B6","article-title":"Efficient policy learning","author":"Athey,","year":"2019","journal-title":"arXiv:"},{"key":"2021051519491947400_B7","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1017\/S0266466608080225","article-title":"Fast rates for estimation error and oracle inequalities for model selection","volume":"24","author":"Bartlett,","year":"2008","journal-title":"Economet. Theory"},{"key":"2021051519491947400_B8","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00440-005-0462-3","article-title":"Empirical minimization","volume":"135","author":"Bartlett,","year":"2006","journal-title":"Prob. Theory Rel. Fields"},{"key":"2021051519491947400_B9","doi-asserted-by":"crossref","first-page":"233","DOI":"10.3982\/ECTA12723","article-title":"Program evaluation and causal inference with high-dimensional data","volume":"85","author":"Belloni,","year":"2017","journal-title":"Econometrica"},{"key":"2021051519491947400_B10","author":"Bickel,","year":"1993","journal-title":"Efficient and Adaptive Estimation for Semiparametric Models"},{"key":"2021051519491947400_B11","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF00117832","article-title":"Stacked regressions","volume":"24","author":"Breiman,","year":"1996","journal-title":"Mach. Learn."},{"key":"2021051519491947400_B12","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10208-006-0196-8","article-title":"Optimal rates for the regularized least-squares algorithm","volume":"7","author":"Caponnetto,","year":"2007","journal-title":"Foundat. Comp. Math."},{"key":"2021051519491947400_B13","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1145\/2939672.2939785","article-title":"XGBoost: A scalable tree boosting system","author":"Chen,","year":"2016","journal-title":"Proc. 22nd ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining (KDD\u201916)"},{"key":"2021051519491947400_B14","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."},{"key":"2021051519491947400_B15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-01-00923-5","article-title":"On the mathematical foundations of learning","volume":"39","author":"Cucker,","year":"2002","journal-title":"Bull. Am. Math. Soc."},{"key":"2021051519491947400_B16","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1080\/01621459.2017.1407322","article-title":"Decomposing treatment effect variation","volume":"114","author":"Ding,","year":"2019","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1214\/18-STS667","article-title":"Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition","volume":"34","author":"Dorie,","year":"2019","journal-title":"Statist. Sci."},{"key":"2021051519491947400_B18","first-page":"1097","article-title":"Doubly robust policy evaluation and learning","author":"Dud\u00edk,","year":"2011","journal-title":"Proc. 28th Int. Conf. Machine Learning (ICML\u201911)"},{"key":"2021051519491947400_B19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v079.i03","article-title":"Kernel-based regularized least squares in R (KRLS) and Stata (krls)","volume":"79","author":"Ferwerda,","year":"2017","journal-title":"J. Statist. Software"},{"key":"2021051519491947400_B20","article-title":"Orthogonal statistical learning","author":"Foster,","year":"2019","journal-title":"arXiv:"},{"key":"2021051519491947400_B21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v033.i01","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"Friedman,","year":"2010","journal-title":"J. Statist. Software"},{"key":"2021051519491947400_B22","first-page":"1","article-title":"Multivariate adaptive regression splines","volume":"19","author":"Friedman,","year":"1991","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B23","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1214\/19-BA1195","article-title":"Bayesian regression tree models for causal inference: Regularization, confounding, and heterogeneous effects","volume":"15","author":"Hahn,","year":"2020","journal-title":"Bayesian Anal."},{"key":"2021051519491947400_B24","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1198\/jcgs.2010.08162","article-title":"Bayesian nonparametric modeling for causal inference","volume":"20","author":"Hill,","year":"2011","journal-title":"J. Comp. Graph. Statist."},{"key":"2021051519491947400_B25","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.3982\/ECTA6630","article-title":"Asymptotics for statistical treatment rules","volume":"77","author":"Hirano,","year":"2009","journal-title":"Econometrica"},{"key":"2021051519491947400_B26","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1214\/12-AOAS593","article-title":"Estimating treatment effect heterogeneity in randomized program evaluation","volume":"7","author":"Imai,","year":"2013","journal-title":"Ann. Appl. Statist."},{"key":"2021051519491947400_B27","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","author":"Imbens,","year":"2015","journal-title":"Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction"},{"key":"2021051519491947400_B28","article-title":"Optimal doubly robust estimation of heterogeneous causal effects","author":"Kennedy,","year":"2020","journal-title":"arXiv:"},{"key":"2021051519491947400_B29","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3982\/ECTA13288","article-title":"Who should be treated? Empirical welfare maximization methods for treatment choice","volume":"86","author":"Kitagawa,","year":"2018","journal-title":"Econometrica"},{"key":"2021051519491947400_B30","doi-asserted-by":"crossref","first-page":"4156","DOI":"10.1073\/pnas.1804597116","article-title":"Metalearners for estimating heterogeneous treatment effects using machine learning","volume":"116","author":"K\u00fcnzel,","year":"2019","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2021051519491947400_B31","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1093\/biomet\/asv028","article-title":"Tree-based methods for individualized treatment regimes","volume":"102","author":"Laber,","year":"2015","journal-title":"Biometrika"},{"key":"2021051519491947400_B32","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1515\/ijb-2015-0007","article-title":"Optimal individualized treatments in resource-limited settings","volume":"12","author":"Luedtke,","year":"2016","journal-title":"Int. J. Biostatist."},{"key":"2021051519491947400_B33","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1214\/15-AOS1384","article-title":"Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy","volume":"44","author":"Luedtke,","year":"2016","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B34","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1515\/ijb-2015-0052","article-title":"Super-learning of an optimal dynamic treatment rule","volume":"12","author":"Luedtke,","year":"2016","journal-title":"Int. J. Biostatist."},{"key":"2021051519491947400_B35","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1214\/09-AOS728","article-title":"Regularization in kernel learning","volume":"38","author":"Mendelson,","year":"2010","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B36","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.2307\/2951752","article-title":"The asymptotic variance of semiparametric estimators","volume":"62","author":"Newey,","year":"1994","journal-title":"Econometrica"},{"key":"2021051519491947400_B37","first-page":"1","article-title":"Sur les applications de la th\u00e9orie des probabilit\u00e9s aux experiences agricoles: Essai des principes","volume":"10","author":"Neyman,","year":"1923","journal-title":"Roczniki Nauk Rolniczych"},{"key":"2021051519491947400_B38","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1056\/NEJMp1606181","article-title":"Predicting the future\u2014big data, machine learning, and clinical medicine","volume":"375","author":"Obermeyer,","year":"2016","journal-title":"New Engl. J. Med."},{"key":"2021051519491947400_B39","doi-asserted-by":"crossref","first-page":"1767","DOI":"10.1002\/sim.7623","article-title":"Some methods for heterogeneous treatment effect estimation in high dimensions","volume":"37","author":"Powers,","year":"2018","journal-title":"Statist. Med."},{"key":"2021051519491947400_B40","year":"2021","journal-title":"R: A Language and Environment for Statistical Computing"},{"key":"2021051519491947400_B41","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/978-1-4419-9076-1_11","article-title":"Optimal structural nested models for optimal sequential decisions","author":"Robins,","year":"2004","journal-title":"Proc. 2nd Seattle Sympos. Biostatistics"},{"key":"2021051519491947400_B42","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1214\/16-AOS1515","article-title":"Minimax estimation of a functional on a structured high-dimensional model","volume":"45","author":"Robins,","year":"2017","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B43","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1080\/01621459.1995.10476494","article-title":"Semiparametric efficiency in multivariate regression models with missing data","volume":"90","author":"Robins,","year":"1995","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B44","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2307\/1912705","article-title":"Root-${N}$-consistent semiparametric regression","volume":"56","author":"Robinson,","year":"1988","journal-title":"Econometrica"},{"key":"2021051519491947400_B45","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","article-title":"The central role of the propensity score in observational studies for causal effects","volume":"70","author":"Rosenbaum,","year":"1983","journal-title":"Biometrika"},{"key":"2021051519491947400_B46","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":"J. Educ. Psychol."},{"key":"2021051519491947400_B47","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1080\/01621459.1999.10473862","article-title":"Adjusting for nonignorable drop-out using semiparametric nonresponse models","volume":"94","author":"Scharfstein,","year":"1999","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B48","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1214\/aos\/1176350055","article-title":"On asymptotically efficient estimation in semiparametric models","volume":"14","author":"Schick,","year":"1986","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B49","first-page":"3076","article-title":"Estimating individual treatment effect: Generalization bounds and algorithms","volume":"70","author":"Shalit,","year":"2017","journal-title":"Proc. Mach. Learn. Res."},{"key":"2021051519491947400_B50","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1142\/S0219530503000089","article-title":"Estimating the approximation error in learning theory","volume":"1","author":"Smale,","year":"2003","journal-title":"Anal. Appl."},{"key":"2021051519491947400_B51","author":"Steinwart,","year":"2008","journal-title":"Support Vector Machines"},{"key":"2021051519491947400_B52","article-title":"Optimal rates for regularized least squares regression","author":"Steinwart,","year":"2009","journal-title":"22nd Conference on Learning Theory"},{"key":"2021051519491947400_B53","first-page":"141","article-title":"Subgroup analysis via recursive partitioning","volume":"10","author":"Su,","year":"2009","journal-title":"J. Mach. Learn. Res."},{"key":"2021051519491947400_B54","author":"Talagrand,","year":"2006","journal-title":"The Generic Chaining: Upper and Lower Bounds of Stochastic Processes"},{"key":"2021051519491947400_B55","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1080\/01621459.2014.951443","article-title":"A simple method for estimating interactions between a treatment and a large number of covariates","volume":"109","author":"Tian,","year":"2014","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B56","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani,","year":"1996","journal-title":"J. R. Statist. Soc. B"},{"key":"2021051519491947400_B57","author":"Tsiatis,","year":"2007","journal-title":"Semiparametric Theory and Missing Data"},{"key":"2021051519491947400_B58","article-title":"Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive epsilon-net estimator: Finite sample oracle inequalities and examples","author":"van der Laan,","year":"2003","journal-title":"Tech. rep. UC Berkeley Division of Biostatistics Working Paper Series No. 130"},{"key":"2021051519491947400_B59","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1524\/stnd.2006.24.3.373","article-title":"The cross-validated adaptive epsilon-net estimator","volume":"24","author":"van der Laan,","year":"2006","journal-title":"Statist. Decis."},{"key":"2021051519491947400_B60","article-title":"Super learner","volume":"6","author":"van der Laan,","year":"2007","journal-title":"Statist. Applic. Genet. Molec. Biol."},{"key":"2021051519491947400_B61","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9782-1","author":"van der Laan,","year":"2011","journal-title":"Targeted Learning: Causal Inference for Observational and Experimental Data"},{"issue":"1","key":"2021051519491947400_B62","doi-asserted-by":"crossref","DOI":"10.2202\/1557-4679.1043","article-title":"Targeted maximum likelihood learning","volume":"2","author":"van der Laan,","year":"2006","journal-title":"Int. J. Biostatist."},{"key":"2021051519491947400_B63","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1080\/01621459.2020.1727235","article-title":"Cross-validation, risk estimation, and model selection: Comment on a paper by Rosset and Tibshirani","volume":"115","author":"Wager,","year":"2020","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B64","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1080\/01621459.2017.1319839","article-title":"Estimation and inference of heterogeneous treatment effects using random forests","volume":"113","author":"Wager,","year":"2018","journal-title":"J. Am. Statist. Assoc."},{"key":"2021051519491947400_B65","doi-asserted-by":"crossref","first-page":"12673","DOI":"10.1073\/pnas.1614732113","article-title":"High-dimensional regression adjustments in randomized experiments","volume":"113","author":"Wager,","year":"2016","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2021051519491947400_B66","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0893-6080(05)80023-1","article-title":"Stacked generalization","volume":"5","author":"Wolpert,","year":"1992","journal-title":"Neural Networks"},{"key":"2021051519491947400_B67","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1214\/009053607000000514","article-title":"Consistency of cross validation for comparing regression procedures","volume":"35","author":"Yang,","year":"2007","journal-title":"Ann. Statist."},{"key":"2021051519491947400_B68","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1002\/sta.411","article-title":"Estimating optimal treatment regimes from a classification perspective","volume":"1","author":"Zhang,","year":"2012","journal-title":"Stat."},{"key":"2021051519491947400_B69","article-title":"Selective inference for effect modification via the lasso","author":"Zhao,","year":"2018","journal-title":"arXiv:"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaa076\/35186046\/asaa076.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/2\/299\/37938939\/asaa076.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/2\/299\/37938939\/asaa076.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T09:55:54Z","timestamp":1723542954000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/108\/2\/299\/5911092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,24]]},"references-count":69,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,9,24]]},"published-print":{"date-parts":[[2021,5,15]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa076","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,6,1]]},"published":{"date-parts":[[2020,9,24]]}}}