European Journal of Epidemiology

, Volume 30, Issue 10, pp 1101–1110 | Cite as

Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness

  • Sander Greenland
  • Mohammad Ali MansourniaEmail author


We describe how ordinary interpretations of causal models and causal graphs fail to capture important distinctions among ignorable allocation mechanisms for subject selection or allocation. We illustrate these limitations in the case of random confounding and designs that prevent such confounding. In many experimental designs individual treatment allocations are dependent, and explicit population models are needed to show this dependency. In particular, certain designs impose unfaithful covariate-treatment distributions to prevent random confounding, yet ordinary causal graphs cannot discriminate between these unconfounded designs and confounded studies. Causal models for populations are better suited for displaying these phenomena than are individual-level models, because they allow representation of allocation dependencies as well as outcome dependencies across individuals. Nonetheless, even with this extension, ordinary graphical models still fail to capture distinctions between hypothetical superpopulations (sampling distributions) and observed populations (actual distributions), although potential-outcome models can be adapted to show these distinctions and their consequences.


Causal graphs Confounding Directed acyclic graphs Ignorability Inverse probability weighting Unfaithfulness 



The authors are grateful to the reviewers and Katherine Hoggatt for comments leading to clarification of several key points.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Epidemiology, UCLA School of Public HealthUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of Statistics, UCLA College of Letters and ScienceUniversity of CaliforniaLos AngelesUSA
  3. 3.Department of Epidemiology and Biostatistics, School of Public HealthTehran University of Medical SciencesTehranIran

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