{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T09:18:06Z","timestamp":1780996686888,"version":"3.54.1"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator as a $C_{p}$ criterion using an ignorable treatment assignment condition. Simulation shows that the proposed criterion outperforms a conventional one by providing smaller squared errors and higher frequencies of selecting the true model in all the settings considered. Moreover, in a real-data analysis we found a clear difference between the two criteria.<\/jats:p>","DOI":"10.1093\/biomet\/asx054","type":"journal-article","created":{"date-parts":[[2017,9,8]],"date-time":"2017-09-08T15:11:26Z","timestamp":1504883486000},"page":"845-861","source":"Crossref","is-referenced-by-count":8,"title":["A $C_p$ criterion for semiparametric causal inference"],"prefix":"10.1093","volume":"104","author":[{"given":"Takamichi","family":"Baba","sequence":"first","affiliation":[{"name":"Biostatistics Department, Shionogi & Co., Ltd, 1-1-4 Shibata, Kita-ku, Osaka 530-0012, Japan takamichi.baba@shionogi.co.jp"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takayuki","family":"Kanemori","sequence":"additional","affiliation":[{"name":"Client Service Department, The Toa Reinsurance Co., Ltd, 3-6 Kanda-Surugadai, Chiyoda-ku, Tokyo 101-8703, Japan Kanemori_T@toare.co.jp"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yoshiyuki","family":"Ninomiya","sequence":"additional","affiliation":[{"name":"Institute of Mathematics for Industry, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan nino@imi.kyushu-u.ac.jp"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,10,9]]},"reference":[{"key":"2019071815503582300_B1","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":"2019071815503582300_B2","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.csda.2004.08.013","article-title":"A semiparametric model selection criterion with applications to the marginal structural model.","volume":"50","author":"Brookhart","year":"2006","journal-title":"Comp. 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