Causal Diagrams - Chapter 12 - Introduction - Preliminaries and Statistical Independence

Oct 29, 2026

Causal Diagrams by M. Maria Glymour and Sander Greenland introduces causal graph theory as a framework for reasoning from causal assumptions to statistical associations. The chapter explains basic definitions and assumptions, then develops preliminaries for causal graphs using potential-outcome (counterfactual) causation to distinguish causation from mere association. It formalizes statistical independence via conditional probability across strata, clarifying how unassociated variables relate to the lack of informative changes in outcomes across X levels, and sets up later rules and graphical reasoning.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Introduction

Preliminaries for Causal Graphs

Statistical Independence

Causation and Association

Collider Bias

Summary

Graphical Models

Terminology

Rules Linking Absence of Open Paths to Statistical Independencies

Assumptions and Intentions Underlying the Rules

Causal Diagrams M. Maria Glymour and Sander Greenland Introduction 183 Preliminaries for Causal Graphs 184 Statistical Independence 184 Causation and Association 185 Cotlider Bias 185 Summary 186 Graphical Models 186 Terminology 186 Rules Linking Absence of Open Paths to Statistical Independencies 187 Assumptions and Intwtions Underlying the Rules 190 Graphical Representation of Bias and its Control 191 Sufficient and Mnmally Sufficient Conditorung Some Applications 194 Why Conventional Rules for Confounding Are Not Always Reliable 194 Graphical Analyses of Selection Bias 196 Bias from Intentional Se•ection 196 Survivor Bias 198 Residual Confounding and Bias Quantification 198 Bras from Use of Missing-Data Categories or Indicators 199 Adjusting for an Intermediate Does Not Necessarily Estimate a Direct Effect 200 Instrumental Variables 202 Bias from Conditioning on a Descendant of the Outcome 204 Selection Bias and Matchng in Case-Control Studies 205 Sets 192 Choosing Conditioning Sets to Identify Causal Effects 192 Confounding and Selection Bias 192 How Adjust•ng for Baseine Values Can Bias Ana!yses of Change 206 Caveats and Extensions 208 Conclusion 209 INTRODUCTION Diagrams of causal pathways have tong been used to visually summarize hypothetical relations among variables of interest. Modern causal diagrams, or causal graphs, were more recently devel oped from a mcrgerof graphical probability theory with path diagrams. The resulting theory provides a powerful yet intuitive device for deducing the statistical associations implied by causal relations. Conversely, given a set of observed statistical relations. a researcher armed with causal graph theory can systematically characterize all causal structures compatible with the observations. The theory also provides a visual representation of key concepts in the more general theory or longitudinal causality or Robins ( 1997); see Chapter 21 for further discussion and references on the tatter topic. The graphical rules linking causal relations to statistical associations are grounded in mathe. matics. Hence, one way to think of causal diagrams is that they allow nonmathematicians to draw logically sound conclusions about certain types of statistical relations. Learning the rules for reading statistical associations from causal diagrams may take a little time and practice. Once these rules are mastered, though, they facilitate many tasks, such as understanding confounding and selection 183 Il • bias, choosing covariates for adjustment and for regression analyses, understanding analyses of direct effects and instrumental-variable analyses, and assessing "natural experiments." In particular, diagrams help researchers recognize and avoid common mistakes in causal analysis. This chapter begins with the basic definitions and assumptions used in causal graph theory. It then describes constnction of causal diagrams and the graphical separation rules linking the causal assumptions encoded in a diagram to the statistical relations implied by the diagram. The chapter concludes by presenting some examples of applications. Some readers may prefer to begin with the examples and refer back to the definitions and rules for causal diagrams as needed. The section on Graphical Models, however, is essential to understanding the examples. Full technical details of causal diagrams and their relation to causal inference can be found in Pearl (2000) and Spines et al. (2001), while Greenland and Pearl (2008) provide a short technical review. Less technical articles geared toward health scientists include Greenland et al. (1999a), Robins (2001 ), Greenland and Brumback (2002), Hernán et al. (2002), Jewell (2004), and Glymour (2006b) . PRELIMINARIES FOR CAUSAL GRAPHS Consider two variables X and Y for which we wish to represent a causal connection from X to Y, often phrased as "X causes Y" or "X affects Y. " Causal dia

FAQs

What is the central purpose of causal diagrams in this chapter?

Causal diagrams provide a visual and logically grounded way to deduce the statistical associations implied by causal relations.

How does the chapter distinguish causation from association?

It uses the potential-outcome (counterfactual) concept of causation, where X affects Y only if intervening on X can change Y for at least one unit.

What does statistical independence mean here?

X and Y are statistically independent when the distribution of Y does not differ across strata defined by X, meaning knowing X gives no information about Y.

Oct 29, 2026

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