{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T15:22:54Z","timestamp":1790004174976,"version":"4.0.1"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T00:00:00Z","timestamp":1680134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2022YFA1008100"],"award-info":[{"award-number":["2022YFA1008100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12071015"],"award-info":[{"award-number":["12071015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"crossref","award":["award R01GM139926 to X.S., award R01AI27271, R01AG065276, and R01GM139926"],"award-info":[{"award-number":["award R01GM139926 to X.S., award R01AI27271, R01AG065276, and R01GM139926"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values, also known as \u2018sequential randomization assumption (SRA)\u2019. SRA is often criticized as it requires one to accurately measure all confounders. Realistically, measured covariates can rarely capture all confounders with certainty. Often covariate measurements are at best proxies of confounders, thus invalidating inferences under SRA. In this paper, we extend the proximal causal inference (PCI) framework of Miao, Geng, et al. (2018. Identifying causal effects with proxy variables of an unmeasured confounder. Biometrika, 105(4), 987\u2013993. https:\/\/doi.org\/10.1093\/biomet\/asy038) to the longitudinal setting under a semiparametric marginal structural mean model (MSMM). PCI offers an opportunity to learn about joint causal effects in settings where SRA based on measured time-varying covariates fails, by formally accounting for the covariate measurements as imperfect proxies of underlying confounding mechanisms. We establish nonparametric identification with a pair of time-varying proxies and provide a corresponding characterization of regular and asymptotically linear estimators of the parameter indexing the MSMM, including a rich class of doubly robust estimators, and establish the corresponding semiparametric efficiency bound for the MSMM. Extensive simulation studies and a data application illustrate the finite sample behaviour of proposed methods.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad020","type":"journal-article","created":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T01:20:31Z","timestamp":1680225631000},"page":"684-704","source":"Crossref","is-referenced-by-count":15,"title":["Proximal causal inference for complex longitudinal studies"],"prefix":"10.1093","volume":"85","author":[{"given":"Andrew","family":"Ying","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, The Wharton School, University of Pennsylvania , Philadelphia , United States"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wang","family":"Miao","sequence":"additional","affiliation":[{"name":"Department of Probability and Statistics, Peking University , Beijing , China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xu","family":"Shi","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Michigan , Ann Arbor , United States"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric J","family":"Tchetgen Tchetgen","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, The Wharton School, University of Pennsylvania , Philadelphia , United States"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,3,30]]},"reference":[{"issue":"2","key":"2023071211304822400_qkad020-B1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.jeconom.2017.05.011","article-title":"Examples of L2-complete and boundedly-complete distributions","volume":"199","author":"Andrews","year":"2017","journal-title":"Journal of Econometrics"},{"issue":"2","key":"2023071211304822400_qkad020-B2","doi-asserted-by":"crossref","first-page":"785","DOI":"10.3982\/ECTA9988","article-title":"Local identification of nonparametric and semiparametric models","volume":"82","author":"Chen","year":"2014","journal-title":"Econometrica"},{"issue":"9313","key":"2023071211304822400_qkad020-B3","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/S0140-6736(02)08213-2","article-title":"Methotrexate and mortality in patients with rheumatoid arthritis: A prospective study","volume":"359","author":"Choi","year":"2002","journal-title":"The Lancet"},{"key":"2023071211304822400_qkad020-B4","author":"Cui","year":"2020"},{"issue":"533","key":"2023071211304822400_qkad020-B5","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1080\/01621459.2020.1783272","article-title":"A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity","volume":"116","author":"Cui","year":"2021","journal-title":"Journal of the American Statistical Association"},{"issue":"5","key":"2023071211304822400_qkad020-B6","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.3982\/ECTA6539","article-title":"Nonparametric instrumental regression","volume":"79","author":"Darolles","year":"2011","journal-title":"Econometrica"},{"key":"2023071211304822400_qkad020-B7","author":"Deaner","year":"2020"},{"issue":"3","key":"2023071211304822400_qkad020-B8","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1017\/S0266466610000368","article-title":"On the completeness condition in nonparametric instrumental problems","volume":"27","author":"D\u2019Haultfoeuille","year":"2011","journal-title":"Econometric Theory"},{"issue":"1","key":"2023071211304822400_qkad020-B9","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1097\/EDE.0b013e3181fdcabe","article-title":"A method for detection of residual confounding in time-series and other observational studies","volume":"22","author":"Flanders","year":"2011","journal-title":"Epidemiology"},{"issue":"10","key":"2023071211304822400_qkad020-B10","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1093\/aje\/kwx013","article-title":"A new method for partial correction of residual confounding in time-series and other observational studies","volume":"185","author":"Flanders","year":"2017","journal-title":"American Journal of Epidemiology"},{"issue":"3","key":"2023071211304822400_qkad020-B11","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/biostatistics\/kxr034","article-title":"Using control genes to correct for unwanted variation in microarray data","volume":"13","author":"Gagnon-Bartsch","year":"2012","journal-title":"Biostatistics"},{"key":"2023071211304822400_qkad020-B12","author":"Ghassami","year":"2022"},{"issue":"454","key":"2023071211304822400_qkad020-B13","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1198\/016214501753168154","article-title":"Marginal structural models to estimate the joint causal effect of nonrandomized treatments","volume":"96","author":"Hern\u00e1n","year":"2001","journal-title":"Journal of the American Statistical Association"},{"key":"2023071211304822400_qkad020-B14","volume-title":"Causal inference: What if","author":"Hern\u00e1n","year":"2020"},{"issue":"3","key":"2023071211304822400_qkad020-B15","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1017\/S0266466617000251","article-title":"Nonparametric identification using instrumental variables: Sufficient conditions for completeness","volume":"34","author":"Hu","year":"2018","journal-title":"Econometric Theory"},{"key":"2023071211304822400_qkad020-B16","author":"Kallus","year":"2021"},{"issue":"2","key":"2023071211304822400_qkad020-B17","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1093\/biomet\/ast066","article-title":"Measurement bias and effect restoration in causal inference","volume":"101","author":"Kuroki","year":"2014","journal-title":"Biometrika"},{"issue":"3","key":"2023071211304822400_qkad020-B18","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1097\/EDE.0b013e3181d61eeb","article-title":"Negative controls: A tool for detecting confounding and bias in observational studies","volume":"21","author":"Lipsitch","year":"2010","journal-title":"Epidemiology"},{"key":"2023071211304822400_qkad020-B19","author":"Mastouri","year":"2021"},{"issue":"4","key":"2023071211304822400_qkad020-B20","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1093\/biomet\/asy038","article-title":"Identifying causal effects with proxy variables of an unmeasured confounder","volume":"105","author":"Miao","year":"2018","journal-title":"Biometrika"},{"key":"2023071211304822400_qkad020-B21","author":"Miao","year":"2018"},{"key":"2023071211304822400_qkad020-B22","author":"Michael","year":"2020"},{"issue":"5","key":"2023071211304822400_qkad020-B23","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1111\/1468-0262.00459","article-title":"Instrumental variable estimation of nonparametric models","volume":"71","author":"Newey","year":"2003","journal-title":"Econometrica"},{"issue":"5","key":"2023071211304822400_qkad020-B24","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1097\/00001648-200009000-00011","article-title":"Marginal structural models and causal inference in epidemiology","volume":"11","author":"Robins","year":"2000","journal-title":"Epidemiology"},{"issue":"9\u201312","key":"2023071211304822400_qkad020-B25","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 a sustained exposure period\u2014Application to control of the healthy worker survivor effect","volume":"7","author":"Robins","year":"1986","journal-title":"Mathematical Modelling"},{"key":"2023071211304822400_qkad020-B26","doi-asserted-by":"crossref","first-page":"139S","DOI":"10.1016\/S0021-9681(87)80018-8","article-title":"A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods","volume":"40","author":"Robins","year":"1987","journal-title":"Journal of Chronic Diseases"},{"key":"2023071211304822400_qkad020-B27","author":"Robins","year":"1997"},{"key":"2023071211304822400_qkad020-B28","author":"Robins","year":"1998"},{"issue":"1\/2","key":"2023071211304822400_qkad020-B29","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1023\/A:1005285815569","article-title":"Association, causation, and marginal structural models","volume":"121","author":"Robins","year":"1999","journal-title":"Synthese"},{"key":"2023071211304822400_qkad020-B30","author":"Robins","year":"2000"},{"issue":"2","key":"2023071211304822400_qkad020-B31","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1111\/rssb.12361","article-title":"Multiply robust causal inference with double-negative control adjustment for categorical unmeasured confounding","volume":"82","author":"Shi","year":"2020","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"4","key":"2023071211304822400_qkad020-B32","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1007\/s40471-020-00243-4","article-title":"A selective review of negative control methods in epidemiology","volume":"7","author":"Shi","year":"2020","journal-title":"Current Epidemiology Reports"},{"issue":"3","key":"2023071211304822400_qkad020-B33","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1214\/16-STS558","article-title":"On negative outcome control of unobserved confounding as a generalization of difference-in-differences","volume":"31","author":"Sofer","year":"2016","journal-title":"Statistical Science: A Review Journal of the Institute of Mathematical Statistics"},{"issue":"5","key":"2023071211304822400_qkad020-B34","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1093\/aje\/kwt303","article-title":"The control outcome calibration approach for causal inference with unobserved confounding","volume":"179","author":"Tchetgen Tchetgen","year":"2014","journal-title":"American Journal of Epidemiology"},{"key":"2023071211304822400_qkad020-B35","author":"Tchetgen Tchetgen","year":"2018"},{"key":"2023071211304822400_qkad020-B36","author":"Tchetgen Tchetgen","year":"2020"},{"key":"2023071211304822400_qkad020-B37","author":"Tennenholtz","year":"2020"},{"issue":"5","key":"2023071211304822400_qkad020-B38","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1214\/16-AOS1511","article-title":"Confounder adjustment in multiple hypothesis testing","volume":"45","author":"Wang","year":"2017","journal-title":"Annals of Statistics"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/3\/684\/50859828\/qkad020.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/85\/3\/684\/50859828\/qkad020.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T11:33:43Z","timestamp":1689161623000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/85\/3\/684\/7094061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,30]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3,30]]},"published-print":{"date-parts":[[2023,7,12]]}},"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkad020","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,7]]},"published":{"date-parts":[[2023,3,30]]}}}