Identifying causal effects with causal graphs

Goals

  • Explain how d-separation and causal/noncausal paths relate to identification of causal effects.
  • Apply d-separation to block noncausal paths in causal DAGs with and without unobserved variables.
  • Apply strategies to deal with identification problems caused by unobserved variables.
  • Differentiate confounding and selection bias in terms of graph structure and how they arise in applied studies.





Review

We’ll review pre-class material via the slides here.





Exercises

Exercise 1

For each of the causal graphs below, identify the set of variables needed to block noncausal paths (if possible) between treatment A and outcome Y. Any U variables displayed in the graphs are unobserved/unmeasured.



Exercise 2

Historically, people have tried to create definitions for confounders by listing criteria that purely rely on associations. For example:

A confounder must:
1. Be associated with treatment and outcome
2. Not be caused by treatment

Using the causal graph below, explain why this is not a good definition for a confounder.

Exercise 3

First, think through the relationships depicted in the causal graphs below and whether they make sense. These are intended to reflect a range of scenarios for why people drop out of studies.

Then for each of the graphs, identify the set of variables that would block noncausal paths between the treatment A and outcome Y. (U and W are unmeasured.) Check your answers to one of the graphs using DAGitty.



Exercise 4

In this exercise, we’ll consider how causal graphs can inform study design. (Inspired by a 1970s study on the relationship between estrogen use and endometrial cancer.)

Researchers have noticed a consistent association between use of a certain drug and disease. Research groups debated two hypotheses:

  1. The drug does cause disease.
  2. The drug doesn’t actually cause disease but leads to a side effect, leading to more frequent doctor visits, leading to increased diagnosis of existing disease.

The following study plan was proposed: restrict the study only to those with side effects and compare disease rates in drug-users and non-users. In this way, all participants have the same chance of being diagnosed.

The following causal graphs correspond to the two hypotheses:

(The graphs don’t show confounders of the drug-true disease relationship for compactness. We can assume that these have already been adjusted for.)

Study design 1

Consider the study proposal above: restrict analysis to those with side effects.

  • Before looking at the causal graphs: does the rationale for this study design make sense? Why did researchers want to only look at patients with side effects?

  • Under this study design, the researchers were expecting that if Hypothesis 1 were correct (the drug does cause disease), they would find an association between drug use and diagnosed disease. They expected that if Hypothesis 2 were correct (the drug does NOT cause disease), they would find NO association between drug use and diagnosed disease.

    • Are these expectations correct? Explain in light of the causal graphs.

  • Based on your answer above, is this an effective study design for the research questions of interest? That is, can this study proposal distinguish between the two hypotheses?

Study design 2

Consider another study proposal: ensure that everyone is screened for disease frequently, and we don’t restrict our analysis to only those with side effects.

  • What arrow can be removed as a result of this study design? (It might help to draw an updated version of DAGs 1 and 2 with this arrow removed.)

  • Under this study design, the researchers had the same expectations: if Hypothesis 1 were correct, they would find an association between drug use and diagnosed disease. If Hypothesis 2 were correct, they would find NO association between drug use and diagnosed disease.

    • Are these expectations correct? Explain in light of the causal graphs.

  • Based on your answer above, is this an effective study design for the research questions of interest? That is, can this study proposal distinguish between the two hypotheses?