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Review
. 2010 Feb 26;6(2):Article 7.
doi: 10.2202/1557-4679.1203.

An introduction to causal inference

Judea Pearl  1
Affiliations
Review

An introduction to causal inference

Judea Pearl. Int J Biostat. .

Abstract

This paper summarizes recent advances in causal inference and underscores the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underlie all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: those about (1) the effects of potential interventions, (2) probabilities of counterfactuals, and (3) direct and indirect effects (also known as "mediation"). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both. The tools are demonstrated in the analyses of mediation, causes of effects, and probabilities of causation.

Keywords: causal effects; causes of effects; confounding; counterfactuals; graphical methods; mediation; policy evaluation; potential-outcome; structural equation models.

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Figures

Figure 1:
Figure 1:
A simple structural equation model, and its associated diagrams. Unobserved exogenous variables are connected by dashed arrows.
Figure 2:
Figure 2:
(a) The diagram associated with the structural model of Eq. (5). (b) The diagram associated with the modified model of Eq. (6), representing the intervention do(X = x0).
Figure 3:
Figure 3:
Markovian model illustrating the derivation of the causal effect of X on Y, Eq. (20). Error terms are not shown explicitly.
Figure 4:
Figure 4:
Markovian model illustrating the back-door criterion. Error terms are not shown explicitly.
Figure 5:
Figure 5:
Causal diagram representing the assignment (Z), treatment (X), and outcome (Y) in a clinical trial with imperfect compliance.
Figure 6:
Figure 6:
(a) A generic model depicting mediation through Z with no confounders, and (b) with two confounders, W1 and W2.
Figure 7:
Figure 7:
Stochastic non-linear model of mediation. All variables are binary.
See this image and copyright information in PMC

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