Explanations and answers ARM workgroups ()

Workgroup 1 (03-09-2020)
Goal: In this session, you will practice working with DAGs for the first time: assembling them,
identifying causal and backdoor paths, recognizing the risk of confounder bias. In addition, you
will apply the three conditions for causal inference on a case.

Case 1 ‘the costs of COPD treatment’




The questions
1. Re-visit the DAG language from lecture 1 and the literature. What is the meaning of the
following terms: path, backdoor path, causal path, confounding, collider, blocking and
unblocking?
Path: a route between exposure and outcome, it doesn’t have to follow the direction of the arrows.
Backdoor path an causal path: A causal path follows the direction of the arrows, a backdoor path
does not.
Confounding: Confounding is a bias causes by common cause of exposure and outcome, so a variable
which has an effect on the exposure and the outcome. This can be solved with a confounder, a
variable that can be used to remove it. In other words you adjust the data for the confounding
variable.
Collider: the arrows collide a variable. It’s causes by exposure and outcome.
Blocking and unblocking: you block a path when you adjust for a variable along the path and you
open a path when you adjust for a collider of remove the adjusting from the variable along an open
path. Unblocking is opening the backdoor path by adjusting for the collider, this creates a bias
(always wrong).

! Our aim would be to close backdoor paths during the quantitative parts. This is something which
often gets lost during the way.




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, 2. In what circumstances do you draw an arrow in a DAG? When should you decide not to
draw one?
You draw an arrow when you think there is an causal effect or if you think there is causal effect. If
you don’t draw an arrow you automatically say there is no causal effect, so you’re absolutely sure
about it. In reality you can be in a situation where you’re not 100% sure there is no effect, so this
level of certainty doesn’t have to be fully 100% but still quite big.

3. Explain the difference between selection bias (collider bias) and confounding.
Selection bias is a bias created by selecting your respondents on a specific characteristic. Sometimes
you don’t do this on purpose and sometimes you adjust for a collider (opening a backdoor path),
which is wrong. Whereas a confounding bias occurs when you fail to adjust for a common cause of
exposure.

4. For this case, formulate a research question that represents the goal of the researchers.
Is it less expensive to treat COPD patients with exacerbation (verergering) at home compared to a
hospital?

What is the effect on individual healthcare costs of treating COPD exacerbations in the patient’s
home instead of in the hospital?

It’s important you use causal language, it’s an closed question but he is not saying: is there a
association. An open question would be better: which place of treatment is less expensive, home or
hospital?

5. Draw a DAG that represents the causal structure of this case. You can use Microsoft Word
for this exercise.
Step 1 Write your exposure on the left and the outcome on the right side of a sheet of paper.
Step 2 Draw an arrow from exposure to outcome.
Step 3 Add the other elements from the case: ‘Age’, ‘Sex’, ‘Severity of COPD at baseline’.
Step 4 Draw all appropriate arrows between the items in your DAG.

You’re not sure of the effect of sex on cost and effectiveness, so that’s why you still draw an arrow. If
you’re thinking that there is a possibility that the age might influence the severity, you can draw this
arrow.

During the workgroup session:
6. Identify the paths in the DAG. How many do you see?
1: location treatment  cost-effectiveness
2: location treatment  severity of COPD  cost-effectiveness
3: location treatment  age  cost-effectiveness
4: location treatment  age  severity of COPD  cost-effectiveness
5: location treatment  severity of COPD  Sex  cost-effectiveness
6: location treatment  Sex  cost-effectiveness
7: location treatment  severity of COPD  age  costs-effectiveness
8: location treatment  severity of COPD  sex  cost-effectiveness
9: location treatment  age  severity COPD  sex  costs-effectiveness
10: location treatment  sex  severity COPD  age  costs-effectiveness




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, 7. Which of the paths are open? Which are closed?
Closed paths are:
Treatment location  age  severity COPD  sex  costs-effectiveness
Treatment location  sex  severity COPD  age  costs-effectiveness

Severity is a collider, so that’s why it’s a closed path. All the other paths are open.

8. Which of the paths are causal paths? Which are backdoor paths?
Causal paths:
- location treatment  cost-effectiveness

Backdoor paths:
- location treatment  severity of COPD  cost-effectiveness
- location treatment  age  cost-effectiveness
- location treatment  age  severity of COPD  cost-effectiveness
- location treatment  severity of COPD  Sex  cost-effectiveness
- location treatment  Sex  cost-effectiveness
- location treatment  severity of COPD  age  costs-effectiveness
- location treatment  severity of COPD  sex  cost-effectiveness
- location treatment  age  severity COPD  sex  costs-effectiveness
- location treatment  sex  severity COPD  age  costs-effectiveness

9. Identify the confounders and colliders in your DAG.
Sex, Age and severity of COPD are confounders and severity is a collider as well, so a variable can
have more roles

10. For which variables would you adjust in the statistical analysis? Would you expect this to
lead to an unbiased estimate?
For age and sex. This wouldn’t lead to a unbiased estimate, because you adjust for two of the three
confounders but the third one is also a collider.

But you’re looking at the relationship between the location of the treatment to costs-effectiveness,
so then you do adjust it.

When you adjust sex ór age you’re already closing multiple paths. If I would have adjusted for
severity, it wouldn’t be a problem because you already blocked these paths where severity was a
collider.
 It is true that Severity is a collider in some paths. These backdoor paths are opened by
adjusting for Severity. However, if we also adjust for confounders on those paths (Age, Sex),
we close them again (studeersnel)




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