Summary of
“Graphical and Causal Modeling in
Genetics and Epidemiology”
by
Vanessa Didelez
Nuala Sheehan
Hein Stigum
http://folk.uio.no/heins/
May-16
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1
Graphical Models
• Pedigrees
– Compute carrier probability
• Causal Reasoning
– Conditional independence
– Two main types
• Undirected graphs
• Directed acyclic graphs
• Medelian randomization
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2
Introduction
“Close to the edge”
May-16
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3
Associations
• E and D associated if:
E
D
– E causes D
C
– C is a common cause of E and D
E
D
C
E
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D
Confounder
– C is a common effect of E and D
and we condition on C
Collider
H.S.
4
Marginal and conditional dependence
EE+
E and D are:
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Disease
All
C10 %
3%
14 %
3%
Marginally
dependent
H.S.
C+
21 %
21 %
Conditionally
Independent | C
5
Test of H0
• Can test H0 only if
– E and D are conditionally independent, given
the variables we adjust for (C)
C
C
E
D
E
D
Not OK
OK
Need graphic tools!
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6
Graphic tools
“We have the moral edge!”
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7
Undirected Graph
Definition:
A and B are separated by C
if all paths from A to B pass thru C
1
4
2
3
5
Are 1 and 5 separated by 2 ?
Are 1 and 5 separated by 3 ?
Are 1 and 5 separated by 3 and 4 ?
Yes
No
Yes
If 1 and 5 are separated by 2,
then 1 and 5 are conditionally independent given 2
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Example: Chewing tobacco and ulcers
Chewing tobacco % Ulcers
No
10
Yes
14
Age
Young
Old
Chewing tobacco
No
Yes
No
Yes
T
% Ulcers
3
3
21
21
N
500
500
N
300
200
200
300
T and U are marginally
dependent
T and U are conditionally
independent given A
U
T and U are separated by A
A
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Directed Acyclic Graphs, DAGs
1
3
5
Are 1 and 4 separated by 2 ?
2
No
4
Steps:
1. Take ancestral graph of {1,2,4}
2. Moralize the graph
3. Look for separation
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Directed Acyclic Graphs, DAGs
1
3
2
1
1
Are 1 and 4 separated by 2 ?
No
4
3
2
5
Take ancestral graph of {1,2,4}
4
3
Moralize the graph
2
4
Are 1 and 4 separated by 2 ?
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H.S.
No
11
Estrogen and Endometrial cancer
U
D
E
U=unknown uterine abnormality
D=endometrial cancer
E=estrogen
C=vaginal bleeding
A=ascertained cancer
A
C
Null hypothesis: E and D independent. Can we test H0?
Case-control study, condition on A.
Are E and D cond. independent given A?
Does it help to adjust for C?
U
D
E
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A
C
1. Take ancestral graph of {E,D,A}
2. Moralize
3. Separation by A? No
4. Separation by C,A? No
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Test of H0
• Can test H0 only if
– E and D are conditionally independent, given
the variables we adjust for (C)
C
C
E
D
E
D
Not OK
OK
Use tools to verify!
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13
Cause versus Association
• Observe association,
not necessarily causal:
– Confounding
– Reverse causation
– Selection effect
C
E
D
E
D
E
D
S
– Time trends
T
E
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H.S.
D
14
Definitions
• Association
C
– Observing E predicts D
E
• Causation
– Manipulating E predicts D
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D
C
do(E)
D
15
Problem
• Association ≠ causation
• Intervention on association may be
useless
• Randomization not always feasible
• Need causal information from
observational studies
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Mendelian randomization
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Observation versus trial
•
U
Observational study
–
•
E
D
Randomized trial
1.
2.
3.
–
•
all measured confounders adjusted for
Strong effect, compliance
Does not exist
Does not exist
RD if and only if E causes D
U
2
R
1
E
D
3
Medelian randomization
1. Gene/ exposure association strong, or
large N
2. Should not exist, Mendel’s 2. law
3. Must not exist, depends on the function
of the gene
– GD if and only if E causes D
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U
2
G
1
E
D
3
18
Ex: Alcohol and blood pressure
•
U
Observational study
–
–
Alcohol use increases blood pressure
Many ”lifestyle” confounders
A
BP
Alcohol use
alcohol ml/day
• Gene: ALDH2, 2 alleles
– 2,2 type suffer nausea, headache after alcohol
–  low alcohol regardless of lifestyle (U)
40
30
20
10
0
1,1
•
Medelian randomization
1.
2.
3.
–
Gene ALDH2 is highly associated with alcohol
Mendel’s 2. law, no ass. to obs. confounders
OK, gene function is known
Result: 2,2 type BP +7.4 mmHg
G
A
BP
3
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H.S.
2,2
U
2
1
1,2
Genotype
19
Violations of core conditions
1. Gene/exposure association
•
•
Gene rare or weak effect  large N
Compensation
2. and 3. Gene independent of U and D
•
•
•
Pleiotropy
Linkage disequilibrium
Population stratification
U
2
G
1
E
D
3
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20