{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T21:57:40Z","timestamp":1780955860250,"version":"3.54.1"},"reference-count":78,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable nonparametric estimator exists for marginal structural models with multi-valued or continuous time-varying treatments. In this paper, we combine flexible, data-adaptive regression methods, including ensemble learning techniques, with recent developments in semiparametric efficiency theory for longitudinal studies to propose such an estimator. The proposed estimator is based on a study of the nonparametric identifying functional, including first-order von Mises expansions, as well as the efficient influence function and the efficiency bound. We show conditions under which the proposed estimators are efficient, asymptotically normal and sequentially doubly robust. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on a COVID-19 dataset, studying the impact of mobility on the cumulative number of observed cases.<\/jats:p>","DOI":"10.1093\/biomet\/asag026","type":"journal-article","created":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T11:46:28Z","timestamp":1775216788000},"source":"Crossref","is-referenced-by-count":0,"title":["Nonparametric efficient estimation of marginal structural models with continuous time-varying treatments"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4665-9113","authenticated-orcid":false,"given":"A","family":"Martin","sequence":"first","affiliation":[{"name":"Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine , 180 Madison Avenue , New York, New York 10016,","place":["U.S.A"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0599-3876","authenticated-orcid":false,"given":"M","family":"Santacatterina","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine , 180 Madison Avenue , New York, New York 10016,","place":["U.S.A"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9056-2047","authenticated-orcid":false,"given":"I","family":"D\u00edaz","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine , 180 Madison Avenue , New York, New York 10016,","place":["U.S.A"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"2026060816591294600_asag026-B1","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1093\/biomet\/asx054","article-title":"A criterion for semiparametric causal inference","volume":"104","author":"Baba","year":"2017","journal-title":"Biometrika"},{"key":"2026060816591294600_asag026-B2","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":"2026060816591294600_asag026-B4","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1093\/biomet\/asx053","article-title":"Doubly robust nonparametric inference on the average treatment effect","volume":"104","author":"Benkeser","year":"2017","journal-title":"Biometrika"},{"key":"2026060816591294600_asag026-B3","first-page":"689","volume-title":"Proc. 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