{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T02:50:44Z","timestamp":1787799044952,"version":"build-2784847793"},"reference-count":58,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T00:00:00Z","timestamp":1640649600000},"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":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Causal mediation analysis concerns the pathways through which a treatment affects an outcome. While most of the mediation literature focuses on settings with a single mediator, a flourishing line of research has examined settings involving multiple mediators, under which path-specific effects (PSEs) are often of interest. We consider estimation of PSEs when the treatment effect operates through K(\u2265 1) causally ordered, possibly multivariate mediators. In this setting, the PSEs for many causal paths are not nonparametrically identified, and we focus on a set of PSEs that are identified under Pearl's nonparametric structural equation model. These PSEs are defined as contrasts between the expectations of 2K+1 potential outcomes and identified via what we call the generalized mediation functional (GMF). We introduce an array of regression-imputation, weighting and \u2018hybrid\u2019 estimators, and, in particular, two K + 2-robust and locally semiparametric efficient estimators for the GMF. The latter estimators are well suited to the use of data-adaptive methods for estimating their nuisance functions. We establish the rate conditions required of the nuisance functions for semiparametric efficiency. We also discuss how our framework applies to several estimands that may be of particular interest in empirical applications. The proposed estimators are illustrated with a simulation study and an empirical example.<\/jats:p>","DOI":"10.1111\/rssb.12487","type":"journal-article","created":{"date-parts":[[2021,12,29]],"date-time":"2021-12-29T06:15:41Z","timestamp":1640758541000},"page":"794-821","source":"Crossref","is-referenced-by-count":34,"title":["Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators"],"prefix":"10.1093","volume":"84","author":[{"given":"Xiang","family":"Zhou","sequence":"first","affiliation":[{"name":"Harvard University , Cambridge , Massachusetts , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,12,28]]},"reference":[{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1097\/EDE.0b013e31826c2bb9","article-title":"Mediation analysis for nonlinear models with confounding","volume":"23","author":"Albert","year":"2012","journal-title":"Epidemiology"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1111\/j.1541-0420.2010.01547.x","article-title":"Generalized causal mediation analysis","volume":"67","author":"Albert","year":"2011","journal-title":"Biometrics"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"37","DOI":"10.2307\/2094445","article-title":"The decomposition of effects in path analysis","author":"Alwin","year":"1975","journal-title":"American Sociological Review"},{"key":"2023022408354382400_","volume-title":"Identifiability of path-specific effects","author":"Avin","year":"2005"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","article-title":"Doubly robust estimation in missing data and causal inference models","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"key":"2023022408354382400_","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":"Journal of Personality and Social Psychology"},{"key":"2023022408354382400_","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"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/biom.12248","article-title":"Causal mediation analysis with multiple mediators","volume":"71","author":"Daniel","year":"2015","journal-title":"Biometrics"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1016\/j.jpubeco.2003.11.002","article-title":"Are there civic returns to education","volume":"88,","author":"Dee","year":"2004","journal-title":"Journal of Public Economics,"},{"key":"2023022408354382400_","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":"The International Journal of Biostatistics"},{"key":"2023022408354382400_","first-page":"1","volume-title":"Handbook of labor economics","author":"Fortin","year":"2011"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1111\/j.1467-9868.2008.00673.x","article-title":"Estimation of controlled direct effects","volume":"70","author":"Goetgeluk","year":"2009","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1097\/EDE.0b013e3181c311b2","article-title":"Alternative assumptions for the identification of direct and indirect effects","author":"Hafeman","year":"2011","journal-title":"Epidemiology"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1080\/01621459.2014.880058","article-title":"Multiply robust estimation in regression analysis with missing data","volume":"109","author":"Han","year":"2014","journal-title":"Journal of the American Statistical Association"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1093\/biomet\/ass087","article-title":"Estimation with missing data: beyond double robustness","volume":"100","author":"Han","year":"2013","journal-title":"Biometrika"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s11109-005-3075-8","article-title":"The missing link: exploring the relationship between higher education and political engagement","volume":"27","author":"Hillygus","year":"2005","journal-title":"Political Behavior"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1214\/10-STS321","article-title":"Identification, inference and sensitivity analysis for causal mediation effects","volume":"25","author":"Imai","year":"2010","journal-title":"Statistical Science"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1080\/10410236.2013.873363","article-title":"The health belief model as an explanatory framework in communication research: exploring parallel, serial, and moderated mediation","volume":"30","author":"Jones","year":"2015","journal-title":"Health Communication"},{"key":"2023022408354382400_","first-page":"523","article-title":"Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data","volume":"22","author":"Kang","year":"2007","journal-title":"Statistical Science"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"53","DOI":"10.2307\/3090261","article-title":"Why education matters","author":"Kingston","year":"2003","journal-title":"Sociology of Education"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.2202\/1544-6115.1309","article-title":"Super learner","volume":"6","author":"van der Laan","year":"2007","journal-title":"Statistical Applications in Genetics and Molecular Biology"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.1515\/jci-2015-0027","article-title":"Interventional approach for path-specific effects","volume":"5","author":"Lin","year":"2017","journal-title":"Journal of Causal Inference"},{"key":"2023022408354382400_","volume-title":"Sequential double robustness in right-censored longitudinal models","author":"Luedtke","year":"2017"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1080\/01621459.2017.1295862","article-title":"Quantifying an adherence path-specific effect of antiretroviral therapy in the nigeria pepfar program","volume":"112","author":"Miles","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"2023022408354382400_","first-page":"159","article-title":"On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding","volume":"107","author":"Miles","year":"2020","journal-title":"Biometrika"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1016\/j.jpubeco.2003.10.005","article-title":"Does education improve citizenship? Evidence from the united states and the united kingdom","volume":"88","author":"Milligan","year":"2004","journal-title":"Journal of Public Economics"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1093\/biomet\/asx027","article-title":"Multiple robustness in factorized likelihood models","volume":"104","author":"Molina","year":"2017","journal-title":"Biometrika"},{"key":"2023022408354382400_","first-page":"2112","article-title":"Large sample estimation and hypothesis","volume":"5","author":"Newey","year":"1994","journal-title":"Handbook of Econometrics, IV, Edited by RF Engle and DL McFadden"},{"key":"2023022408354382400_","volume-title":"Cross-fitting and fast remainder rates for semiparametric estimation","author":"Newey","year":"2018"},{"key":"2023022408354382400_","first-page":"1","article-title":"On the application of probability theory to agricultural experiments. Essay on principles. Section 9","volume":"10","author":"Neyman","year":"1923","journal-title":"Annals of Agricultural Sciences"},{"key":"2023022408354382400_","volume-title":"Direct and indirect effects","author":"Pearl","year":"2001"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511803161","volume-title":"Causality: models, reasoning, and inference","author":"Pearl","year":"2009"},{"key":"2023022408354382400_","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":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1177\/0962280210386207","article-title":"Diagnosing and responding to violations in the positivity assumption","volume":"21","author":"Petersen","year":"2012","journal-title":"Statistical Methods in Medical Research"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1093\/oso\/9780198510550.003.0007","article-title":"Semantics of causal dag models and the identification of direct and indirect effects","author":"Robins","year":"2003","journal-title":"Highly Structured Stochastic Systems"},{"key":"2023022408354382400_","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":"2023022408354382400_","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":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1214\/07-STS227D","article-title":"Comment: Performance of double-robust estimators when \u201cinverse probability\u201d weights are highly variable","volume":"22","author":"Robins","year":"2007","journal-title":"Statistical Science"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139058513","volume-title":"Voter turnout: a social theory of political participation","author":"Rolfe","year":"2012"},{"key":"2023022408354382400_","volume-title":"On the multiply robust estimation of the mean of the g-functional","author":"Rotnitzky","year":"2017"},{"key":"2023022408354382400_","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":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316696","volume-title":"Multiple imputation for nonresponse in surveys","author":"Rubin","year":"1987"},{"key":"2023022408354382400_","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":"Journal of the American Statistical Association"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1214\/18-STS647","article-title":"Introduction to double robust methods for incomplete data","volume":"33","author":"Seaman","year":"2018","journal-title":"Statistical Science"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1111\/cogs.12058","article-title":"Counterfactual graphical models for longitudinal mediation analysis with unobserved confounding","volume":"37","author":"Shpitser","year":"2013","journal-title":"Cognitive Science"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1093\/aje\/kwx051","article-title":"Flexible mediation analysis with multiple mediators","volume":"186","author":"Steen","year":"2017","journal-title":"American Journal of Epidemiology"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"4567","DOI":"10.1002\/sim.5864","article-title":"Inverse odds ratio-weighted estimation for causal mediation analysis","volume":"32","author":"Tchetgen Tchetgen","year":"2013","journal-title":"Statistics in Medicine"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1214\/12-AOS990","article-title":"Semiparametric theory for causal mediation analysis: efficiency bounds, multiple robustness, and sensitivity analysis","volume":"40","author":"Tchetgen Tchetgen","year":"2012","journal-title":"Annals of Statistics"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1097\/EDE.0b013e3181bd5638","article-title":"Concerning the consistency assumption in causal inference","volume":"20","author":"VanderWeele","year":"2009","journal-title":"Epidemiology"},{"key":"2023022408354382400_","volume-title":"Explanation in causal inference: methods for mediation and interaction","author":"VanderWeele","year":"2015"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1515\/em-2012-0010","article-title":"Mediation analysis with multiple mediators","volume":"2","author":"VanderWeele","year":"2014","journal-title":"Epidemiologic Methods"},{"key":"2023022408354382400_","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":"2023022408354382400_","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 (Cambridge, Mass.)"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1515\/2161-962X.1014","article-title":"Imputation strategies for the estimation of natural direct and indirect effects","volume":"1","author":"Vansteelandt","year":"2012","journal-title":"Epidemiologic Methods"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1097\/EDE.0000000000001168","article-title":"Effect decomposition in the presence of treatment-induced confounding: a regression-with-residuals approach","volume":"31","author":"Wodtke","year":"2020","journal-title":"Epidemiology"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/978-1-4419-9782-1_27","volume-title":"Targeted learning","author":"Zheng","year":"2011"},{"key":"2023022408354382400_","doi-asserted-by":"crossref","DOI":"10.2202\/1557-4679.1361","article-title":"Targeted maximum likelihood estimation of natural direct effects","volume":"8","author":"Zheng","year":"2012","journal-title":"The International Journal of Biostatistics"},{"key":"2023022408354382400_","doi-asserted-by":"publisher","DOI":"10.31235\/osf.io\/2rx6p","volume-title":"Tracing causal paths from experimental and observational data","author":"Zhou","year":"2020"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12487","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12487","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/84\/3\/794\/49322425\/jrsssb_84_3_794.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/84\/3\/794\/49322425\/jrsssb_84_3_794.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T23:10:03Z","timestamp":1700003403000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/84\/3\/794\/7056148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,28]]},"references-count":58,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,12,28]]},"published-print":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12487","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,7]]},"published":{"date-parts":[[2021,12,28]]}}}