Confounding
and
DAGs
(Directed Acyclic Graphs)
Hein Stigum
Apr-20
H.S.
1
Agenda
• Confounder
• Collider
Causal Knowledge as a Prerequisite for Confounding Evaluation…
Hernán et al. AJE, 2002
Apr-20
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CONFOUNDER DEFINITION
Apr-20
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Associations
• E and D associated
E
D
– E causes D
C
– E and D have common cause
E
D
C
– Both
E
Apr-20
D
• Overall E-D association =
spurious effect from C
+ causal E-D effect
H.S.
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Adjusting is OK
CONFOUNDER EXAMPLES
Apr-20
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Classic confounder
C is the confounder
RRED
is biased
RRED|C is unbiased
C
E
D
age
+
+
vitamins
birth defects
RRED =0.8 positive bias, towards
the null
Adjust for age:
RRED|C=0.5 is unbiased
true biased
0
Apr-20
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1
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Mediated confounder
C
U
E
D
obesity
+
+
age + vitamin birth defects
Apr-20
U is the confounder
C is a confounder mediator
Effect on D is mediated
RRED
is biased
RRED|C is unbiased
RRED =0.8 positive bias,
towards the null
Adjust for obesity:
RRED|C=0.5 is unbiased
H.S.
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Mediated confounder 2
U
C
E
D
gene
+
+
earlier +
birth
vitamin
malform
defects
Apr-20
U is the confounder
C is a confounder mediator
Effect on E is mediated
RRED
is biased
RRED|C is unbiased
RRED =0.8 positive bias,
towards the null
Adjust for earlier malformations:
RRED|C=0.5 is unbiased
H.S.
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Marker for confounder
U
E
D
C
U is the confounder
C is a confounder marker
RRED
is biased
RRED|C is less biased
+
gene - folate - neural tube
+
enzyme
RRED =0.3 negative bias,
away from the null
Adjust for enzyme:
RRED|C=0.5 is less biased
biasedtrue
0
Apr-20
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1
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COLLIDER DEFINITION
Apr-20
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Definition
• Confounder
C
– Common cause for E and D
E
D
C
• Collider
– Common effect of E and D
Apr-20
H.S.
E
D
11
Definition cont.
• Classic
E
D
C
+
diet
cancer + weight loss
Apr-20
C is a collider, no confounding
RRED
is unbiased
RRED|C is biased
• Example
RRED =1.0 cancer not diet related
Positive collider=negative bias?
Adjust for weight loss:
RRED|C=0.8 is biased
H.S.
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Adjusting is not OK
COLLIDER EXAMPLES
Apr-20
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Classic collider
E
D
C
folate - preterm + LBW
Apr-20
C is a collider,
There is no confounding
RRED
is unbiased
RRED|C is biased
RRED =0.5 is unbiased
Negative collider=positive bias?
Adjust for low birth weight (LBW):
RRED|C=0.8 is biased
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Shared cause
U
E
D
C
Low age
+
vitamin -
Apr-20
birth +
LBW
defects
C is a collider of U and D
C and E has a shared cause
RRED
is unbiased
RRUD|C is biased
RRED|C is biased
RRED =0.8 is unbiased
Adjust for low birth weight (LBW):
Positive bias, towards the null?
RRED|C=1.0 is biased
H.S.
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Shared cause 2
U
E
D
C
C is a collider of U and E
C and D has a shared cause
RRED
is unbiased
RREU|C is biased
RRED|C is biased
gene
+
vitamin -
+
birth
defects
+
Apr-20
RRED =0.8 is unbiased
maternal Adjust for maternal weight gain:
weight Negative bias, away from the null?
gain
RRED|C=0.5 is biased
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Folate-neural tube study
• Case Control study
– Exposure:
– Disease:
– ORED=0.65
folate intake
neural tube defects
Should we restrict analysis to live births?
– ORED|C=0.80
Apr-20
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Graph 1, collider
folate - neural tube + stillbirth
Apr-20
RRED =0.65 is unbiased
Adjust for stillbirth:
Positive bias, towards the null
RRED|C=0.8 is biased
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Graph 2, confounder marker
+
RRED =0.65 is biased
stillbirths + folate neural tube Adjust for stillbirth:
Positive bias, towards the null
+
stillbirth RRED|C=0.8 is unbiased
Opposite conclusion as graph 1
Apr-20
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SUMMING UP
Apr-20
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Confounder versus Collider
• Confounder
– Common cause for E and D
– or some variant thereof
– Adjust
C
E
D
• Collider
– Common effect of E and D
– or some variant thereof
– Not adjust
Apr-20
H.S.
C
E
D
21
Collider
• Common effect of:
E
D
C
E and D
U
E
D
C
cause of E and D
U
E
C
D
E and cause of D
Reasons not to adjust for C
• C is a collider
• C is a weak confounder and
– C has missing
– C has errors
– C is highly correlated with other cofactors
Apr-20
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The birth weight “paradox” uncovered, Hernández-Díaz at al. AJE,
2006
COLLIDER EXAMPLE
Apr-20
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Birth weight distribution
Apr-20
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Infant mortality
Apr-20
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To adjust or not adjust
• Crude
– RRsmoke=1.55 (1.50, 1.59)
• Adjusted for birth weight
– RRsmoke=1.09 (1.05, 1.12)
Should we adjust for birth weight?
Apr-20
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A likely DAG
U
E
C
D
C is a collider of U and E
C and D has a shared cause
RRED
is unbiased
RREU|C is biased
RRED|C is biased
U
+
+
U: malnutrition, malformation
smoke + LBW + mort
+
Apr-20
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DAG simplified
U
+
+
smoke + LBW
mort
RRED
is unbiased =1.0
RREU|C is biased
<1.0
RRED|C is biased
<1.0
Negative bias
U
+
+
Same direction of bias
smoke + LBW + mort
+
Apr-20
biased
0
H.S.
1.09
true
1.55
29
Summing up
• Confounding
smoke
yellow
fingers
– “Yellow fingers”-”lung cancer”
association is useful
– not causal
lung
cancer
• Collider
U
+
+
smoke + LBW + mort
+
Apr-20
– Among Low Birth Weight children
“smokers” do better, less likely
that the cause of LBW is
malformation
– “smoking” does not protect
against mortality
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