{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T19:44:49Z","timestamp":1790538289300,"version":"4.1.0"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2011,8,9]],"date-time":"2011-08-09T00:00:00Z","timestamp":1312848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Danish Natural Science Research Council","award":["09-072331"],"award-info":[{"award-number":["09-072331"]}]},{"name":"Interuniversity Attraction Pole research network","award":["P06\/03"],"award-info":[{"award-number":["P06\/03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We extend the definition of the controlled direct effect of a point exposure on a survival outcome, other than through some given, time-fixed intermediate variable, to the additive hazard scale. We propose two-stage estimators for this effect when the exposure is dichotomous and randomly assigned and when the association between the intermediate variable and the survival outcome is confounded only by measured factors, which may themselves be affected by the exposure. The first stage of the estimation procedure involves assessing the effect of the intermediate variable on the survival outcome via Aalen\u2019s additive regression for the event time, given exposure, intermediate variable and confounders. The second stage involves applying Aalen\u2019s additive model, given the exposure alone, to a modified stochastic process (i.e. a modification of the observed counting process based on the first-stage estimates). We give the large sample properties of the estimator proposed and investigate its small sample properties by Monte Carlo simulation. A real data example is provided for illustration.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2011.00782.x","type":"journal-article","created":{"date-parts":[[2011,8,9]],"date-time":"2011-08-09T14:54:48Z","timestamp":1312901688000},"page":"773-788","source":"Crossref","is-referenced-by-count":41,"title":["Estimation of Direct Effects for Survival Data by using the Aalen Additive Hazards Model"],"prefix":"10.1093","volume":"73","author":[{"given":"Torben","family":"Martinussen","sequence":"first","affiliation":[{"name":"University of Copenhagen , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stijn","family":"Vansteelandt","sequence":"additional","affiliation":[{"name":"Ghent University , Belgium, and London School of Hygiene and Tropical Medicine , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mette","family":"Gerster","sequence":"additional","affiliation":[{"name":"University of Southern Denmark , Odense , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacob von Bornemann","family":"Hjelmborg","sequence":"additional","affiliation":[{"name":"University of Southern Denmark , Odense , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2011,8,9]]},"reference":[{"key":"2023031107163065200_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4615-7397-5_1","article-title":"A model for non-parametric regression analysis of counting processes","volume":"2","author":"Aalen","year":"1980","journal-title":"Lect. 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