Causal Graphs, DAGs

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Causal Graphs, DAGs

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

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Agenda

• Background
• Concepts
• Confounder, Collider, causal DAG
• Analyzing DAGs
• Paths open/closed, causal/biasing
• Conditioning
• Examples/Exercises

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Background
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Purpose

• Purpose
• .... investigate .... association between ......
• True purpose
• Process to disease
• Do interventions
• Designs
• Experiment ? cause
• Observation ? cause ?

Cause
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Statistics and causality

• Statistics
• R Fisher only associations
• New movement
• J Pearl (2000) Causality

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Error

• Random error
• Source sampling
• Expressed as precision
• p-values
• Confidence intervals

• Systematic error
• Source design
• Expressed as bias
• Selection bias
• Information bias
• Confounding
• Affect
• Frequency measure
• Association measure

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Precision, Bias and Casual Effect
The true value of an association The Causal
Effect
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New concepts, methods

• Concepts
• Counterfactual definition of causality
• Collider new bias
• Time dependent confounding new situation
• Methods
• Inverse prob. Weighting control confounding
• Marginal Structural models regression
• Causal graphs (DAGs)

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god-DAG
C age
U obesity
Notation Time
E vitamin
D birth defects
Questions on the DAG E-D effect without
bias? Adjust for age?
DAGDirected Acyclic Graph
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DAGs

• Directed Acyclic Graphs
• Transform causal relations into associations
• Conditions association causal effect
• Guide analysis (adjust or not)
• Convey ideas
• Understand concepts
• Confounding
• Selection bias
• Information bias

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Concepts

• Causal versus casual

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Association and Cause
Causal structure
Association
Lung cancer
Yellow fingers
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Confounder, Collider

• C is a common cause of E and D
• C is a common effect of E and D (bias if we
  condition on C)

Confounder
Collider
Condition on stratify restrict adjust
Bias Selection Information Confounding
Collider
Confounder
Hernan et al, A structural approach to selection
bias, Epidemiology 2004
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Confounder idea
A common cause
Smoking


Yellow fingers
Lung cancer

• A confounder induces an association between its
  effects
• Conditioning on a confounder removes the
  association
• Condition (restrict, stratify, adjust)
• Bias direction?

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Collider idea
Two causes for limping
Limp


Hip arthritis
Knee injury

• Conditioning on a collider induces an association
  between the causes
• Condition (restrict, stratify, adjust)
• Bias direction?

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Analyzing DAGS Paths

• The Path of the Righteous

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Paths, unconditional
Definitions
U lifestyle
C cholesterol
Paths from E to D Causal path E?.?.?D Closed
path ?.?
E statin
D CHD
CHDCoronary Heart Disease
Is C a collider?
Yes, on at least one path
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Paths, conditioning
Conditioning on
U lifestyle
C cholesterol
a noncollider closes ?.??
a collider opens ?.? (or a descendant of a
collider)
E statin
D CHD
Goal Close all noncausal paths, keep causal
paths of interest open
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Exercise Statin and CHD
Given the paths described on the previous
slides, answer the following

• You want the total effect of statin on CHD. What
  would you adjust for?
• Can we estimate the direct effect of statin on
  CHD (not mediated through cholesterol)?

U lifestyle
C cholesterol
E statin
D CHD
5 minutes
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Confounding
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Vitamin and birth defects
Bias in E-D? Adjust for C?
C age
U obesity
Goal Close all nocausal paths, keep causal paths
of interest open
E vitamin
D birth defects
Bias
No bias
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Exercise Physical activity and Coronary Heart
Disease (CHD)
C1 age

• We want the total effect of Physical Activity on
  CHD. What should we adjust for?

E Phys. Act.
D CHD
C2 sex
5 minutes
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Selection bias
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Selection bias
S0/1, S1 selected All analyzes conditional on
S1
S
In the population E?S?D, noncausal, closed
E
D
S
In the sample E?S?D, noncausal, open
E
D
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Response bias

• Random
• Selective
• Differential

R
E
D
R
E
D
R
E
D
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Education and Alzheimer
Study the effect of education on Alzheimer among
high prestige jobs
I intelligence
Background Intelligence protects from
Alzheimer. Education and intelligence are
compensatory for a high prestige job lack one,
need more of the other.
S prestige job
E education
D Alzheimer
Paths E?D causal open E?S?I?D noncausal open
Have selection bias in the sample.
Paths E?D causal open E?S?I?D noncausal clo
sed
Now adjust for intelligence
!
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Exercise Survivior bias

• Study exposure early in life (E) on later disease
  (D) among survivors (S)
• Early exposure decreases survival
• A risk factor (R) increases later disease and
  reduces survival
• Draw and analyze the DAG

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Exercise M-structure

• Show the paths
• Should we adjust for C?
• If the design implies a selection on C, what
  would you call the resulting bias selection bias
  or confounding?

A
B
C
E
D
5 minutes
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Information bias

• Measurement error

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Error in E

• Want effect of E on D
• Analyze E on D
• E is the effect of the true E and the error
  process UE
• Can test H0
• E associated with D iff E causes D

UE
E
E
D
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Error in E and D

• Want effect of E on D
• Analyze E on D
• E is the effect of the true E and the error
  process UE
• D is the effect of the true D and the error
  process UD
• Can test H0
• E associated with D iff E causes D

UE
UD
E
D
E
D
Independent, non-differential errors
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Measurement error bias

• Can not test H0
• E associated with D even when E is independent
  of D

UED
UE
UD
UE
UD
UE
UD
E
E
D
E
D
D
E
D
E
D
E
D
Dependent errors
Differential errors
Differential errors
Common cause of errors Temperature influence
both errors
Case-control with dependent recall Alcohol in
pregnancy and malformations
Cohort with investigator bias Diagnoser not
blinded to exposure
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Whats missing

• Path
• E?E?D?D
• Known Linear regression
• No bias from random error in D
• Bias towards null from random error in E
• Known Logistic regression
• Bias towards null from random error in either E
  or D
• But, at present
• Direction and size of error can not be read of
  the DAG

UE
UD
E
D
E
D
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Summing up

• DAGs
• Causal relation translate into associations
• Pro
• Simple, flexible tool. Few basic rules.
• Unified framework to evaluate design and analysis
• Con
• No rules to find the true causal DAG

Better discussion based on DAGs
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References

• 1 Rothman KJ, Greenland S, Lash TL. Modern
  Epidemiology. 3. ed. Philadelphia Lippincott
  Willams Williams,2008.
• 2 Greenland S, Pearl J, Robins JM. Causal
  diagrams for epidemiologic research. Epidemiology
  1999 10 37-48.
• 3 Hernan MA, Hernandez-Diaz S, Robins JM. A
  structural approach to selection bias.
  Epidemiology 2004 15 615-25.
• 4 Hernan MA, Robins JM. A structural approach to
  observation bias. American Journal of
  Epidemiology 2005 161 S100.
• 5 Hernandez-Diaz S, Schisterman EF, Hernan MA.
  The birth weight "paradox" uncovered? Am J
  Epidemiol 2006 164 1115-20.
• 6 Schisterman EF, Cole SR, Platt RW.
  Overadjustment Bias and Unnecessary Adjustment in
  Epidemiologic Studies. Epidemiology 2009 20
  488-95.
• 7 VanderWeele TJ, Hernan MA, Robins JM. Causal
  directed acyclic graphs and the direction of
  unmeasured confounding bias. Epidemiology 2008
  19 720-8.
• 8 VanderWeele TJ, Robins JM. Four types of
  effect modification - A classification based on
  directed acyclic graphs. Epidemiology 2007 18
  561-8.
• 9 Weinberg CR. Can DAGs clarify effect
  modification? Epidemiology 2007 18 569-72.

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