ABSTRACT
Chapter 5 explains directed acyclic graphs and their use in encoding conditional independence assumptions and in causal inference. The concept of d-separation is introduced together with four basic graphical structures (chain, fork, collider, and descendant of a collider), and then a theorem that relates d-separation to conditional independence is stated. The graphical concept of faithfulness is introduced. The four causal structures: intermediate variable, common cause, common effect, and effect of a common effect are related to the four basic graphical structures. The backdoor theorem is presented together with its use in identifying a sufficient set of confounders and its implications for overturning the traditional definition of confounder as a variable associated with the exposure and the outcome. The chapter defines a true confounder and explains that when there is no true confounder, there is no confounding; however, sometimes a sufficient set of confounders can be found that does not contain a true confounder. Methods for simulating data are related to causal directed acyclic graphs, and different methods for generating confounding are contrasted. The chapter shows how to place potential outcomes on a causal directed acyclic graph, thus reconciling the two frameworks. Examples and R code are also provided.
