Slide 1Confounding is a type of bias where variables X and Y share a common cause, Z, that explains some or all of the relationship between X and Y. You're likely familiar with examples of confounding like ice cream sales and violent crime.

Slide 2If you look just in the data, it looks like increases in ice cream sales could be causing increases in violent crime, or maybe the other way around. But this is what we call a spurious correlation. Ice cream sales and violent crime are both more common when the weather is warm. Once you statistically control for weather, let's say by looking just at sales on hot days, there is no relationship between ice cream sales and crime.

Slide 3Causal relationships observed in non-experimental contexts are at high risk of confounding, and the goal of confounder-control studies is to find and statistically adjust for a sufficient set of variables to eliminate confounding.

Slide 4That takes more than statistics, because data are profoundly dumb. A dataset cannot tell you which variables to adjust for, or what is a cause and what is an effect. For that you need information that lives outside of statistical models. You need causal models that are informed by domain expertise.

Slide 5For this reason, a graphical approach based on causal diagrams has emerged as a popular tool for causal inference in confounder-control studies. The most common type of graphical model you'll encounter is the causal directed acyclic graph, or DAG. Causal diagrams turn up outside confounder-control work as well, but this is where you see them used most often.

Slide 6Here is an example DAG of the effect of taking the road less traveled on happiness. As a graph, a DAG consists of nodes and edges. The nodes are the variables, and the edges are the arrows between them. Each arrow makes a causal statement.

Slide 7DAGs have been framed as storytelling devices. The story I am telling with this DAG is that the road traveled causes happiness directly, and indirectly, by creating new social relationships. This DAG also shows my assumption that happiness and the decision to take the road less traveled are both caused in part by one's cognitive style, for example a sense of optimism. They share a common cause. Happiness is also caused by income which, like cognition, is a function of background characteristics like genetics and family.

Slide 8Before I even do anything with this DAG, or any DAG I create, I've accomplished a lot just by drawing my assumptions. The DAG represents my belief in the data generating process. It includes all nodes and connections that I believe are relevant to the effect of road traveled on happiness. I've made my assumptions clear and can proceed to identify how I will estimate the causal effect of interest.

Slide 9Now you might call bull, and that's OK. You can draw a different DAG that might have different implications for the best analysis strategy. You and I should be able to defend our assumptions and be open to modifications based on subject matter criticism. But whether you draw a DAG or not, there is no escaping the need to make assumptions. DAGs just help to make your assumptions clear and transparent.

Slide 10As a graph, DAGs consist of nodes and edges, or arrows. Nodes are variables, like our exposure of interest, the road traveled, and our outcome of interest, happiness later in life. Nodes can take any form, from discrete values of road traveled, more traveled or less traveled, to continuous values of income. A DAG can include observed, measured variables and unobserved variables, including background factors such as genetics.

Slide 11Nodes are connected by edges, directed arrows that make causal statements about how two variables are related. For instance, by drawing an arrow from road traveled to happiness, I'm asserting that the road one travels causes happiness. Arrows do not indicate whether this relationship is positive or negative, just that road traveled influences happiness. Equivalently, the absence of an arrow between nodes implies that there is no causal relationship.

Slide 12The only hard rule in a DAG is that cycles are not permitted. Arrows can go into and out of a node, but there must not be any recursive pathways. Social relationships causing happiness, and happiness causing social relationships back again, is not allowed. Causal effects must only flow forward in time.

Slide 13There are three possible relationship structures in a DAG, and the first is a fork. In a fork, like the one on screen, where cognition points to both road traveled and happiness, cognition is a common cause of the two focal variables of interest. So cognition confounds the causal effect of road traveled on happiness. Some, or all, of the observed association is due to cognition. When you see a fork, you should think confounding.

Slide 14The second structure is a pipe. Pipes, or chains, involve mediator variables like social relationships that represent an indirect causal chain of effects. Road traveled causes new social relationships, which cause happiness. Whether or not you are interested in the indirect causal effect depends on your research question. Often we care about the total causal effect, which includes the direct effect and all the indirect, mediated effects. Sometimes, however, an aim of a study will be to understand possible mechanisms of action that involve mediated pathways.

Slide 15The third structure is a collider. Colliders, or inverted forks, are closed pathways, like road traveled pointing to an active lifestyle and happiness also pointing to an active lifestyle, where a node on the pathway only has incoming arrows. These pathways are closed by default, and they only open when you condition on the collider, which distorts the relationship between road traveled and happiness. As you will see shortly, being able to recognize these three relationships will help you to identify your causal effect of interest.

Slide 16In order to use a DAG to identify a causal effect, you must include all of the relevant nodes and paths. As you can probably imagine, this can get out of hand quickly. Just look at this slide, which diagrams the American military's perceived challenge in its war in Afghanistan. War is hard, and so is drawing everything that matters.

Slide 17DAG creation has been framed as a balancing act. On one hand, we want to omit from the diagram every variable and arrow we can possibly get away with. The simpler the diagram is, the easier it is to understand, and the more likely it is that we'll be able to figure out how to identify the answer to our research question. On the other hand, omitting things makes the model simpler, and the real world is complex. So in our quest for simplicity, we might end up leaving out something that's really important.

Slide 18A piece of practical advice is to draw a basic DAG and then add additional variables, or nodes, only if you believe they causally affect two or more existing nodes in the DAG. For instance, maybe you could argue that being left handed also contributes to one's decision to take the road less traveled. If handedness does not have an arrow into any other nodes, you can safely leave it out of the DAG.

Slide 19If this feels daunting, you're doing it right. Science is hard, and I predict that you'll find this process easier if you have the humility to know that, at best, your study will approximate the truth. There is a very good chance that your DAG will be wrong or incomplete. Your colleagues might tell you as much. This is part of the scientific process. Criticism should lead you to revise your DAG or strengthen how you defend your assumptions.