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Biometrika Advance Access first published online on February 7, 2007
This version published online on February 19, 2007
Biometrika, doi:10.1093/biomet/asm005
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Copyright © Biometrika Trust

Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable

Manabu Kuroki

Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama-cho, Toyonaka, Osaka, 560-8531, Japan

mkuroki{at}sigmath.es.osaka

Received for publication 1 March 2005. Revision received 1 May 2006.
  Abstract

We consider the problem of using data in studies with an unobserved treatment/response variable in order to evaluate average causal effects, when cause-effect relationships between variables can be described by a directed acyclic graph and the corresponding recursive factorization of a joint distribution. The paper proposes graphical criteria to test whether average causal effects are identifiable even if a treatment/response variable is unobserved. If the answer is affirmative, we provide further formulations for average causal effects from the observed data. The graphical criteria enable us to evaluate average causal effects when it is difficult to observe a treatment/response variable.

Key Words: Back door criterion • Causal diagram • Causal effect • Indicator

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