{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T04:02:53Z","timestamp":1791518573550,"version":"4.3.4"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2022,2,8]],"date-time":"2022-02-08T00:00:00Z","timestamp":1644278400000},"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":[[2022,11,29]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem stating that in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment probabilities. We also consider a number of parametric models for interference and find that our nonparametric indirect effect remains a natural estimand when re-expressed in the context of these models.<\/jats:p>","DOI":"10.1093\/biomet\/asac008","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T12:11:34Z","timestamp":1643371894000},"page":"1165-1172","source":"Crossref","is-referenced-by-count":30,"title":["Average direct and indirect causal effects under interference"],"prefix":"10.1093","volume":"109","author":[{"given":"Yuchen","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Management Science and Engineering, Stanford University , 475 Via Ortega, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuangning","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University , 390 Jane Stanford Way, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","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":[[2022,2,8]]},"reference":[{"key":"2022112917593003000_B1","doi-asserted-by":"crossref","first-page":"1912","DOI":"10.1214\/16-AOAS1005","article-title":"Estimating average causal effects under general interference, with application to a social network experiment","volume":"11","author":"Aronow,","year":"2017","journal-title":"Ann. 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