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On the Consistency Rule in Causal Inference: Axiom, Definition, Assumption, or Theorem?

Pearl, Judea


Pearl J. On the consistency rule in causal inference: axiom, definition, assumption, or theorem? Epidemiology. 2010;21:872–875.

Reference 13 in this paper was originally published in Polish in 1923 and then in English in 1990. The correct citation for the English version is as follows:

13. Splawa-Neyman J. On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Statist Sci. 1990;5:465–472.

Epidemiology. 22(2):285, March 2011.

doi: 10.1097/EDE.0b013e3181f5d3fd
Methods: Brief Report

In 2 recent communications, Cole and Frangakis (Epidemiology. 2009;20:3–5) and VanderWeele (Epidemiology. 2009;20:880–883) conclude that the consistency rule used in causal inference is an assumption that precludes any side-effects of treatment/exposure on the outcomes of interest. They further develop auxiliary notation to make this assumption formal and explicit. I argue that the consistency rule is a theorem in the logic of counterfactuals and need not be altered. Instead, warnings of potential side-effects should be embodied in standard modeling practices that make causal assumptions explicit and transparent.

From the Department of Computer Science, University of California, Los Angeles, CA.

Submitted 9 February 2010; accepted 23 April 2010.

Supported partially by NIH grants 1R01 LM009961–01, NSF grants IIS-0914211, and ONR grants N000–14–09–1-0665.

Correspondence: 4532 Boelter Hall, Department of Computer Science, University of California, Los Angeles, CA 90095–1596. E-mail:

© 2010 Lippincott Williams & Wilkins, Inc.