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Directed acyclic graphs with edge-specific bounds

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  • Tyler J. Vanderweele
  • Zhiqiang Tan

Abstract

We give a definition of a bounded edge within the causal directed acyclic graph framework. A bounded edge generalizes the notion of a signed edge and is defined in terms of bounds on a ratio of survivor probabilities. We derive rules concerning the propagation of bounds. Bounds on causal effects in the presence of unmeasured confounding are also derived using bounds related to specific edges on a graph. We illustrate the theory developed by an example concerning estimating the effect of antihistamine treatment on asthma in the presence of unmeasured confounding. Copyright 2012, Oxford University Press.

Suggested Citation

  • Tyler J. Vanderweele & Zhiqiang Tan, 2012. "Directed acyclic graphs with edge-specific bounds," Biometrika, Biometrika Trust, vol. 99(1), pages 115-126.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:115-126
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    File URL: http://hdl.handle.net/10.1093/biomet/asr059
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