{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T23:17:00Z","timestamp":1793143020178,"version":"4.5.0"},"reference-count":67,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T00:00:00Z","timestamp":1602806400000},"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":[[2021,8,12]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two asymptotically optimal nonparametric estimators that leverage data-adaptive regression for the estimation of nuisance parameters: a one-step estimator and a targeted minimum loss estimator. We further present results establishing the conditions under which these estimators are consistent, multiply robust, $n^{1\/2}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on risky behaviour in adolescent girls.<\/jats:p>","DOI":"10.1093\/biomet\/asaa085","type":"journal-article","created":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T03:31:18Z","timestamp":1601609478000},"page":"627-641","source":"Crossref","is-referenced-by-count":54,"title":["Nonparametric efficient causal mediation with intermediate confounders"],"prefix":"10.1093","volume":"108","author":[{"given":"I","family":"D\u00edaz","sequence":"first","affiliation":[{"name":"Division of Biostatistics, Department of Healthcare Policy & Research, Weill Cornell Medicine, 425 East 61st Street, New York, New York 10065, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N S","family":"Hejazi","sequence":"additional","affiliation":[{"name":"Division of Epidemiology & Biostatistics, School of Public Health, University of California, Berkeley, 2121 Berkeley Way, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K E","family":"Rudolph","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, Mailman School of Public Health, Columbia University, 722 West 168th Street, New York, New York 10032, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M J","family":"van Der Laan","sequence":"additional","affiliation":[{"name":"Division of Epidemiology & Biostatistics, School of Public Health, University of California, Berkeley, 2121 Berkeley Way, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,10,16]]},"reference":[{"key":"2021081218511563900_B1","first-page":"357","article-title":"Identifiability of path-specific effects","author":"Avin,","year":"2005","journal-title":"Proc. 19th Int. Joint Conf. Artificial Intelligence (IJCAI'05)"},{"key":"2021081218511563900_B2","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1037\/0022-3514.51.6.1173","article-title":"The moderator\u2013mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations","volume":"51","author":"Baron,","year":"1986","journal-title":"J. Pers. Soc. Psychol."},{"key":"2021081218511563900_B3","article-title":"Nonparametric inference for interventional effects with multiple mediators","author":"Benkeser,","year":"2020","journal-title":"arXiv:"},{"key":"2021081218511563900_B4","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/DSAA.2016.93","article-title":"The highly adaptive lasso estimator","author":"Benkeser,","year":"2016","journal-title":"2016 IEEE Int. Conf. Data Science and Advanced Analytics (DSAA)"},{"key":"2021081218511563900_B5","author":"Bickel,","year":"1997","journal-title":"Efficient and Adaptive Estimation for Semiparametric Models"},{"key":"2021081218511563900_B6","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1214\/08-AOS620","article-title":"Simultaneous analysis of lasso and Dantzig selector","volume":"37","author":"Bickel,","year":"2009","journal-title":"Ann. Statist."},{"key":"2021081218511563900_B7","first-page":"1","article-title":"mice: Multivariate imputation by chained equations in R","volume":"45","author":"Buuren,","year":"2010","journal-title":"J. Statist. Software"},{"key":"2021081218511563900_B8","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1109\/18.749011","article-title":"Improved rates and asymptotic normality for nonparametric neural network estimators","volume":"45","author":"Chen,","year":"1999","journal-title":"IEEE Trans. Info. Theory"},{"key":"2021081218511563900_B9","article-title":"Double\/debiased machine learning for treatment and causal parameters","author":"Chernozhukov,","year":"2017","journal-title":"arXiv:"},{"key":"2021081218511563900_B10","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1093\/ije\/31.1.163","article-title":"Fallibility in estimating direct effects","volume":"31","author":"Cole,","year":"2002","journal-title":"Int. J. Epidemiol."},{"key":"2021081218511563900_B11","author":"Coyle,","year":"2020","journal-title":"sl3: Modern Pipelines for Machine Learning and Super Learning"},{"key":"2021081218511563900_B12","author":"Coyle,","year":"2019","journal-title":"hal9001: The Scalable Highly Adaptive Lasso"},{"key":"2021081218511563900_B13","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/01621459.2000.10474210","article-title":"Causal inference without counterfactuals","volume":"95","author":"Dawid,","year":"2000","journal-title":"J. Am. Statist. Assoc."},{"key":"2021081218511563900_B14","article-title":"Super learner based conditional density estimation with application to marginal structural models","volume":"7","author":"D\u00edaz,","year":"2011","journal-title":"Int. J. Biostatist."},{"key":"2021081218511563900_B15","first-page":"138","article-title":"Direct and indirect effects of sequential treatments","author":"Didelez,","year":"2006","journal-title":"Proc. 22nd Conf. Uncertainty in Artificial Intelligence (UAI'06)"},{"key":"2021081218511563900_B16","first-page":"1","article-title":"Multivariate adaptive regression splines","volume":"19","author":"Friedman,","year":"1991","journal-title":"Ann. Statist."},{"key":"2021081218511563900_B17","doi-asserted-by":"crossref","first-page":"979","DOI":"10.2307\/1913851","article-title":"Structural equation methods in the social sciences","volume":"40","author":"Goldberger,","year":"1972","journal-title":"Econometrica"},{"key":"2021081218511563900_B18","author":"Hejazi,","year":"2020","journal-title":"medoutcon: Efficient Causal Mediation Analysis under Intermediate Confounding"},{"key":"2021081218511563900_B19","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1037\/a0020761","article-title":"A general approach to causal mediation analysis","volume":"15","author":"Imai,","year":"2010","journal-title":"Psychol. Meth."},{"key":"2021081218511563900_B20","doi-asserted-by":"crossref","first-page":"2800","DOI":"10.1214\/17-EJS1302","article-title":"Converting high-dimensional regression to high-dimensional conditional density estimation","volume":"11","author":"Izbicki,","year":"2017","journal-title":"Electron. J. Statist."},{"key":"2021081218511563900_B21","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1214\/aos\/1176350609","article-title":"Consistent estimation of the influence function of locally asymptotically linear estimators","volume":"15","author":"Klaassen,","year":"1987","journal-title":"Ann. Statist."},{"key":"2021081218511563900_B22","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1111\/j.1468-0262.2007.00733.x","article-title":"Experimental analysis of neighborhood effects","volume":"75","author":"Kling,","year":"2007","journal-title":"Econometrica"},{"key":"2021081218511563900_B23","doi-asserted-by":"crossref","first-page":"4008","DOI":"10.1002\/sim.6990","article-title":"Defining and estimating causal direct and indirect effects when setting the mediator to specific values is not feasible","volume":"35","author":"Lok,","year":"2016","journal-title":"Statist. Med."},{"key":"2021081218511563900_B24","article-title":"Causal organic direct and indirect effects: Closer to Baron and Kenny with a product method for binary mediators","author":"Lok,","year":"2020","journal-title":"arXiv:"},{"key":"2021081218511563900_B25","article-title":"On partial identification of the pure direct effect","author":"Miles,","year":"2015","journal-title":"arXiv:"},{"key":"2021081218511563900_B26","article-title":"Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn","author":"Nguyen,","year":"2020","journal-title":"arXiv:"},{"key":"2021081218511563900_B27","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1542\/peds.2011-2535","article-title":"Gender and crime victimization modify neighborhood effects on adolescent mental health","volume":"130","author":"Osypuk,","year":"2012","journal-title":"Pediatrics"},{"key":"2021081218511563900_B28","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1093\/biomet\/82.4.669","article-title":"Causal diagrams for empirical research","volume":"82","author":"Pearl,","year":"1995","journal-title":"Biometrika"},{"key":"2021081218511563900_B29","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1177\/0049124198027002004","article-title":"Graphs, causality, and structural equation models","volume":"27","author":"Pearl,","year":"1998","journal-title":"Sociolog. Meth. Res."},{"key":"2021081218511563900_B30","author":"Pearl,","year":"2000","journal-title":"Causality: Models, Reasoning, and Inference"},{"key":"2021081218511563900_B31","first-page":"411","article-title":"Direct & indirect effects","author":"Pearl,","year":"2001","journal-title":"Proc. 17th Conf. Uncertainty in Artificial Intelligence (UAI'01)"},{"key":"2021081218511563900_B32","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1097\/01.ede.0000208475.99429.2d","article-title":"Estimation of direct causal effects","volume":"17","author":"Petersen,","year":"2006","journal-title":"Epidemiology"},{"key":"2021081218511563900_B33","first-page":"379","article-title":"Contributions to a general asymptotic statistical theory","volume":"3","author":"Pfanzagl,","year":"1985","journal-title":"Statist. Risk Mod."},{"key":"2021081218511563900_B34","author":"Popper,","year":"1934","journal-title":"The Logic of Scientific Discovery"},{"key":"2021081218511563900_B35","year":"2021","journal-title":"R: A Language and Environment for Statistical Computing"},{"key":"2021081218511563900_B36","article-title":"Single world intervention graphs (SWIGs): A unification of the counterfactual and graphical approaches to causality","author":"Richardson,","year":"2013"},{"key":"2021081218511563900_B37","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1016\/0270-0255(86)90088-6","article-title":"A new approach to causal inference in mortality studies with sustained exposure periods\u2014application to control of the healthy worker survivor effect","volume":"7","author":"Robins,","year":"1986","journal-title":"Math. Mod."},{"key":"2021081218511563900_B38","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1097\/00001648-199203000-00013","article-title":"Identifiability and exchangeability for direct and indirect effects","volume":"3","author":"Robins,","year":"1992","journal-title":"Epidemiology"},{"key":"2021081218511563900_B39","first-page":"103","article-title":"Alternative graphical causal models and the identification of direct effects","author":"Robins,","year":"2010","journal-title":"Causality and Psychopathology: Finding the Determinants of Disorders and Their Cures"},{"key":"2021081218511563900_B40","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1097\/EDE.0000000000000774","article-title":"Composition or context: Using transportability to understand drivers of site differences in a large-scale housing experiment","volume":"29","author":"Rudolph,","year":"2018","journal-title":"Epidemiology"},{"key":"2021081218511563900_B41","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1097\/EDE.0000000000000832","article-title":"Mediation of neighborhood effects on adolescent substance use by the school and peer environments","volume":"29","author":"Rudolph,","year":"2018","journal-title":"Epidemiology"},{"key":"2021081218511563900_B42","article-title":"Robust and flexible estimation of stochastic mediation effects: A proposed method and example in a randomized trial setting","volume":"7","author":"Rudolph,","year":"2017","journal-title":"Epidemiol. Meth."},{"key":"2021081218511563900_B43","author":"Spirtes,","year":"2000","journal-title":"Causation, Prediction, and Search"},{"key":"2021081218511563900_B44","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1097\/EDE.0000000000000154","article-title":"Bounds for pure direct effect","volume":"25","author":"Tchetgen Tchetgen,","year":"2014","journal-title":"Epidemiology"},{"key":"2021081218511563900_B45","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1097\/EDE.0000000000000054","article-title":"On identification of natural direct effects when a confounder of the mediator is directly affected by exposure","volume":"25","author":"Tchetgen Tchetgen,","year":"2014","journal-title":"Epidemiology"},{"key":"2021081218511563900_B46","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":"2021081218511563900_B47","article-title":"Robust variance estimation and inference for causal effect estimation","author":"Tran,","year":"2018","journal-title":"arXiv:"},{"key":"2021081218511563900_B48","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":"2021081218511563900_B49","doi-asserted-by":"crossref","DOI":"10.2202\/1557-4679.1064","article-title":"Direct effect models","volume":"4","author":"van der Laan,","year":"2008","journal-title":"Int. J. Biostatist."},{"key":"2021081218511563900_B50","doi-asserted-by":"crossref","DOI":"10.2202\/1544-6115.1309","article-title":"Super learner","volume":"6","author":"van der Laan,","year":"2007","journal-title":"Statist. Appl. Genet. Molec. Biol."},{"key":"2021081218511563900_B51","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21700-0","author":"van der Laan,","year":"2003","journal-title":"Unified Methods for Censored Longitudinal Data and Causality"},{"key":"2021081218511563900_B52","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"},{"key":"2021081218511563900_B53","author":"van der Laan,","year":"2018","journal-title":"Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies"},{"key":"2021081218511563900_B54","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":"2021081218511563900_B55","first-page":"331","article-title":"Semiparametric statistics","author":"van der Vaart,","year":"2002","journal-title":"Lectures on Probability Theory and Statistics"},{"key":"2021081218511563900_B56","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1524\/stnd.2006.24.3.351","article-title":"Oracle inequalities for multi-fold cross-validation","volume":"24","author":"van der Vaart,","year":"2006","journal-title":"Statist. Decis."},{"key":"2021081218511563900_B57","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1097\/EDE.0000000000000034","article-title":"Effect decomposition in the presence of an exposure-induced mediator-outcome confounder","volume":"25","author":"VanderWeele,","year":"2014","journal-title":"Epidemiology"},{"key":"2021081218511563900_B58","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1097\/EDE.0000000000000596","article-title":"Interventional effects for mediation analysis with multiple mediators","volume":"28","author":"Vansteelandt,","year":"2017","journal-title":"Epidemiology"},{"key":"2021081218511563900_B59","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1111\/j.1541-0420.2012.01777.x","article-title":"Natural direct and indirect effects on the exposed: Effect decomposition under weaker assumptions","volume":"68","author":"Vansteelandt,","year":"2012","journal-title":"Biometrics"},{"key":"2021081218511563900_B60","first-page":"749","article-title":"SVM method of estimating density, conditional probability, and conditional density","volume":"2","author":"Vapnik,","year":"2000","journal-title":"2000 IEEE Int. Sympos. Circuits and Systems"},{"key":"2021081218511563900_B61","article-title":"Adaptive concentration of regression trees, with application to random forests","author":"Wager,","year":"2016","journal-title":"arXiv:"},{"key":"2021081218511563900_B62","first-page":"557","article-title":"Correlation and causation","volume":"20","author":"Wright,","year":"1921","journal-title":"J. Agric. Res."},{"key":"2021081218511563900_B63","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1214\/aoms\/1177732676","article-title":"The method of path coefficients","volume":"5","author":"Wright,","year":"1934","journal-title":"Ann. Math. Statist."},{"key":"2021081218511563900_B64","doi-asserted-by":"crossref","DOI":"10.1515\/jci-2016-0006","article-title":"Longitudinal mediation analysis with time-varying mediators and exposures, with application to survival outcomes","volume":"5","author":"Zheng,","year":"2017","journal-title":"J. Causal Infer."},{"key":"2021081218511563900_B65","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/978-1-4419-9782-1_27","article-title":"Cross-validated targeted minimum-loss-based estimation","author":"Zheng,","year":"2011","journal-title":"Targeted Learning"},{"key":"2021081218511563900_B66","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2202\/1557-4679.1361","article-title":"Targeted maximum likelihood estimation of natural direct effects","volume":"8","author":"Zheng,","year":"2012","journal-title":"Int. J. Biostatist."},{"key":"2021081218511563900_B67","author":"Zill,","year":"1990","journal-title":"Behavior Problems Index Based on Parent Report"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/3\/627\/39711388\/asaa085.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaa085\/36169818\/asaa085.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/3\/627\/39711388\/asaa085.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T10:11:07Z","timestamp":1723716667000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/108\/3\/627\/5924585"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,16]]},"references-count":67,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,10,16]]},"published-print":{"date-parts":[[2021,8,12]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa085","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,9,1]]},"published":{"date-parts":[[2020,10,16]]}}}