Transcript Causal Diagrams in Epi Analysis

Using Directed Acyclic Graphs
(DAGs) to assess confounding
Glenys Webster & Anne Harris
May 14, 2007
St Paul’s Hospital Statistical “Rounds”
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
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?)
Has anyone used DAGs
before?
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
What is confounding?
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
C
E
D
E.g. E = yellow fingers, D = lung cancer, C = smoking
How to assess confounding?
3 commonly used methods:
1. Automatic variable selection (p values)
2. Compare adjusted vs unadjusted ORs
3. Check criteria for confounding
Confounders are:
 Associated with E
 Associated with D (in unexposed)
 Not in the causal pathway between E & D
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
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
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)
C
E
D
Directed Acyclic Graphs (DAGs)
• Directed: Arrows show “causal direction”
of association
• Acyclic: No feedback loops between E
& D (following direction of arrows)
C
E
D
C
E
D
Variable definitions
•
•
•
•
E = Exposure
D = Disease
C = Potential confounder
U = Unmeasured variable
U
C
E
D
DAGs terminology
• Ancestor, Parent
• Descendent, Child
• Common ancestor = Common cause = Confounder
• Common descendent = Common effect = Collider
C
E
D
E
D
C
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
Example 1: C = common cause
C
E
D
Step 1: Remove arrow between E  D
Example 1: C = common cause
C
E
D
Step 2: Look for backdoor pathways between E & D
Example 1: C = common cause
C
E
D
Backdoor path exists!  need to adjust for C
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
Example 2:
C = common effect (collider)
E
D
C
Step 1: Remove arrow between E  D
Example 2:
C = common effect (collider)
E
D
C
Step 2: Look for backdoor pathways between E & D
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!
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
Fig 5
C
E
D
Fig 6
U
C
E
D
Fig 7
U
C
E
D
Fig 8
U
E
D
C
Fig 1
E
D
C
Fig 2
U1
E
D
C
Fig 3
E
U2
D
C
Fig 4
U1
E
U2
D
C
Exercise results
Figure
1
2
3
4
5
6
7
8
Adjust for C?
YES
NO







()
What do these graphs
have in common?
What do these graphs
have in common?
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
Example
• Case-control study of folate supplementation
(E) and neural tube defects (D). What should
be done with mystery variable, C?
Folate
No Folate
Neural Tube
Defect
Control Defect
43
239
194
704
Crude OR: 0.65 (CI: 0.45-0.94)
Is Mystery Variable ‘C’ a confounder?
Method 1: Automatic selection
• Build model with D, E and C
• If p value of ßC is < 0.1, keep C in model
– p value of ßC = 0.001
Conclusion: Adjust for C
Is Mystery Variable ‘C’ a confounder?
Method 2: Change in effect size
• Compare adjusted and unadjusted ORs
• If the difference is > 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
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
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
ORC=1: 1.09
Neural
Tube
Defect
Control
Defect
Folate
24
231
No Folate
94
658
ORC=0: 0.72
Adjusted OR = 0.80 (95% CI: 0.53, 1.20)
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
What is C?
• Stillbirth or therapeutic abortion (C=1)
• Live birth (C=0)
C
E
D
E
D
C
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.
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
Discussion