Using Directed Acyclic Graphs (DAGs) to assess confounding

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Using Directed Acyclic Graphs (DAGs) to assess
confounding

• Glenys Webster Anne Harris
• May 14, 2007
• St Pauls Hospital Statistical Rounds

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The Issue

• Confounding introduces bias into effect estimates
• Common methods to assess confounding can
• Fail to identify confounders ? residual bias
• Introduce bias by adjusting for non-confounders
• Graphical causal models (e.g. DAGs) can help
• Hernan, MA 2002. Am J of Epidemiol 155 (2)
  176-184

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Objective

• Introduce a graphical method to help assess
  potential confounders
• Directed Acyclic Graphs (DAGs)
• Useful during
• Study design (which variables to measure?)
• Data analysis (which variables to adjust for?)

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Has anyone used DAGs before?
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Overview

• Review common methods to assess confounding
• Introduce Directed Acyclic Graphs (DAGs)
• Exercise Spot the confounders!
• Example Folate vs neural tube defects
• Why incorporating a priori knowledge (using DAGs)
  matters
• Conclusions Discussion

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What is confounding?
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What is confounding?

• Occurs when the relationship observed between E
  D is at least partly due to another variable (C)
• Occurs when E D share a common cause

E.g. E yellow fingers, D lung cancer, C
smoking
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How to assess confounding?

• 3 commonly used methods
• Automatic variable selection (p values)
• Compare adjusted vs unadjusted ORs
• Check criteria for confounding
• Confounders are
• Associated with E
• Associated with D (in unexposed)
• Not in the causal pathway between E D

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BUT!

• These methods may lead to bias1-4 by
• Omitting important confounders
• Adjusting for non-confounders
• Limited consideration of causal mechanisms
• Graphical models (e.g. DAGs) can help

1. Weinberg CR 1993. Am J Epidemiol 137 1-8
2. Greenland S et al. 1999. Epidemiology 10 37-48
3. Robins JM. 2001. Epidemiology 12 313-320
4. Pearl J. 2000. Causality. Cambridge University
   Press

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Directed Acyclic Graphs (DAGs)

• Picture showing relationships among variables
• Incorporate a priori knowledge
• Clearly state assumptions
• Helps to identify
• Which variables to measure
• Confounders Non-confounders
• Proper control for confounding reduces bias

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Directed Acyclic Graphs (DAGs)

• Nodes (variables) and arrows
• Arrows indicate causal direction
• Arrows say nothing about the magnitude, shape or
  the mathematical direction of the association
  (i.e. positive, negative)

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Directed Acyclic Graphs (DAGs)

• Directed Arrows show causal direction of
  association
• Acyclic No feedback loops between E D
  (following direction of arrows)

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Variable definitions

• E Exposure
• D Disease
• C Potential confounder
• U Unmeasured variable

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DAGs terminology

• Ancestor, Parent
• Descendent, Child
• Common ancestor Common cause Confounder
• Common descendent Common effect Collider

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Using DAGs to assess confounding

• Draw a DAG
• Remove arrow between E ? D
• Are there any open backdoor pathways to get
  from E to D?
• If yes ? confounding ? need to adjust
• If no ? no confounding ? do not adjust!
• Rules
• Can follow arrows in any direction
• Colliders (common effects) BLOCK a path
• Adjusting for a non-collider BLOCKs the path
• Adjusting for a collider OPENs the path

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Example 1 C common cause
C
E
D
Step 1 Remove arrow between E ? D
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Example 1 C common cause
C
E
D
Step 2 Look for backdoor pathways between E D
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Example 1 C common cause
C
E
D
Backdoor path exists! ? need to adjust for C
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Example 1 C common cause
C
E
D
Adjusting for C blocks the backdoor pathway from
E to D. There is no more confounding. Observed E
? D relationship is free of bias
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Example 2 C common effect (collider)
E
D
C
Step 1 Remove arrow between E ? D
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Example 2 C common effect (collider)
E
D
C
Step 2 Look for backdoor pathways between E D
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Example 2 C common effect (collider)
E
D
C

• C is a collider ? Blocks the path
• No backdoor pathway ? do not adjust for C
• Adjusting for C would open the pathway,
  INTRODUCE BIAS!

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Spot the confounders (see handout)

• For each graph, should we adjust for C?
• Remove arrow between E ? D
• Are there any open backdoor pathways to get
  from E to D?
• If yes ? confounding ? need to adjust
• If no ? no confounding ? Do not adjust!
• Rules
• Can follow arrows in any direction
• Colliders BLOCK a path
• Adjusting for a non-collider BLOCKs the path
• Adjusting for a collider OPENs the path

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Fig 5
C
E
D
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Fig 6
U
C
E
D
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Fig 7
U
C
E
D
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Fig 8
U
E
D
C
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Fig 1
E
D
C
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Fig 2
U1
E
D
C
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Fig 3
E
D
C
U2
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Fig 4
U1
E
D
C
U2
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Exercise results
Adjust for C? Adjust for C?
Figure YES NO
1 ?
2 ?
3 ?
4 ?
5 ?
6 ?
7 ?
8 (?)
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Incorporating a priori knowledge

• DAGs incorporate our a priori knowledge about how
  variables are related
• Ignoring this knowledge (e.g. using standard
  methods to assess confounding) may introduce bias
• ? Example from the birth defects literature

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Example

• Case-control study of folate supplementation (E)
  and neural tube defects (D). What should be done
  with mystery variable, C?

Neural Tube Defect Control Defect
Folate 43 239
No Folate 194 704
Crude OR 0.65 (CI 0.45-0.94)
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Is Mystery Variable C a confounder?

• Method 1 Automatic selection
• Build model with D, E and C
• If p value of ßC is lt 0.1, keep C in model
• p value of ßC 0.001
• Conclusion Adjust for C

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Is Mystery Variable C a confounder?

• Method 2 Change in effect size
• Compare adjusted and unadjusted ORs
• If the difference is gt 10, adjust for C
• Unadjusted OR 0.65
• Adjusted OR 0.80
• (0.8 - 0.65)/0.65 0.23 (23 difference)
• Conclusion Adjust for C

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Is Mystery Variable C a confounder?

• Method 3 Check rules for confounding
• Is C is associated with Folate supplementation
  (E)?
• OR 0.50
• Is C is associated with Neural tube defects in
  people who did not take folate (D)?
• OR 15.22
• Is C in the causal pathway between folate and
  neural tube defects?
• No (based on a priori knowledge)
• Conclusion Adjust for C

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Adjusting for C

• All 3 standard methods ? Adjust for C

C 1
C 0
Neural Tube Defect Control Defect
Folate 19 8
No Folate 100 46
Neural Tube Defect Control Defect
Folate 24 231
No Folate 94 658
ORC1 1.09 ORC0 0.72 Adjusted OR 0.80 (95
CI 0.53, 1.20)
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Adjusting for C

• Compare adjusted OR to crude OR
• ORadjusted 0.80 (CI 0.53, 1.20)
• ORcrude 0.65 (CI 0.45-0.94)
• Was adjustment appropriate?

C
E
D
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What is C?

• Stillbirth or therapeutic abortion (C1)
• Live birth (C0)

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Folate Example Key Points

• Standard methods to assess confounding include
  little a priori knowledge about how variables are
  related
• Standard methods may suggest confounding when it
  is NOT present
• Adjusting for non-confounders (colliders) can
  introduce bias
• A causal model (e.g. a DAG) is required to
  separate colliders from confounders.

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Conclusions

• Common methods to assess confounding can lead to
  bias by
• Omitting important confounders
• Adjusting for non-confounders
• DAGs are used to
• Identify confounders and non-confounders
  (colliders)
• Incorporate a priori knowledge
• Clearly state your mental model of how system
  works
• Allow others to follow your reasoning
• DAGs are useful for study design data analysis

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Discussion