Causal inference, probability theory, and graphical insights



This article is corrected by:

  1. Errata: Correction for ‘Causal inference, probability theory, and graphical insights’ Volume 33, Issue 11, 1980, Article first published online: 8 January 2014

Correspondence to: Stuart G. Baker, Biometry Research Group, National Cancer Institute, Bethesda, MD 20892, U.S.A.



Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.