Summary of Graphical and Causal Modeling in Genetics and Epidemiology by Vanessa Didelez Nuala Sheeh

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Summary ofGraphical and Causal Modeling in
Genetics and Epidemiologyby Vanessa
DidelezNuala Sheehan

• Hein Stigum
• http//folk.uio.no/heins/

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Graphical Models

• Pedigrees
• Compute carrier probability
• Causal Reasoning
• Conditional independence
• Two main types
• Undirected graphs
• Directed acyclic graphs
• Medelian randomization

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Introduction

• Close to the edge

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Associations

• E and D associated if
• E causes D
• C is a common cause of E and D
• C is a common effect of E and D and we condition
  on C

Confounder
Collider
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Marginal and conditional dependence
Conditionally Independent C
Marginally dependent
E and D are
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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)

Not OK
OK
Need graphic tools!
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Graphic tools

• We have the moral edge!

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Undirected Graph
Definition A and B are separated by C if all
paths from A to B pass thru C
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
T and U are marginally dependent
T and U are conditionally independent given A
T and U are separated by A
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Directed Acyclic Graphs, DAGs
1
3
5
Are 1 and 4 separated by 2 ?
No
2
4

• Steps
• Take ancestral graph of 1,2,4
• Moralize the graph
• Look for separation

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Directed Acyclic Graphs, DAGs
1
3
5
Are 1 and 4 separated by 2 ?
No
2
4
1
3
Take ancestral graph of 1,2,4
2
4
1
3
Moralize the graph
2
4
Are 1 and 4 separated by 2 ?
No
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Estrogen and Endometrial cancer
Uunknown uterine abnormality Dendometrial
cancer Eestrogen Cvaginal bleeding Aascertained
cancer
U
D
A
E
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?
1. Take ancestral graph of E,D,A 2. Moralize 3.
Separation by A? 4. Separation by C,A?
No
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)

Not OK
OK
Use tools to verify!
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Cause versus Association

• Observe association, not necessarily causal
• Confounding
• Reverse causation
• Selection effect
• Time trends

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Definitions

• Association
• Observing E predicts D
• Causation
• Manipulating E predicts D

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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

• Observational study
• all measured confounders adjusted for
• Randomized trial
• Strong effect, compliance
• Does not exist
• Does not exist
• R?D if and only if E causes D
• Medelian randomization
• Gene/ exposure association strong, or large N
• Should not exist, Mendels 2. law
• Must not exist, depends on the function of the
  gene
• G?D if and only if E causes D

U
2
E
D
R
1
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U
2
E
D
G
1
3
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Ex Alcohol and blood pressure

• Observational study
• Alcohol use increases blood pressure
• Many lifestyle confounders
• Gene ALDH2, 2 alleles
• 2,2 type suffer nausea, headache after alcohol
• ? low alcohol regardless of lifestyle (U)
• Medelian randomization
• Gene ALDH2 is highly associated with alcohol
• Mendels 2. law, no ass. to obs. confounders
• OK, gene function is known
• Result 2,2 type BP 7.4 mmHg

U
2
A
BP
G
1
3
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Violations of core conditions

• Gene/exposure association
• Gene rare or weak effect ? large N
• Compensation
• and 3. Gene independent of U and D
• Pleiotropy
• Linkage disequilibrium
• Population stratification