1. DAGs intro without exercises 1h Directed Acyclic Graph
Hein Stigum
courses
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2. Motivating example C E D C C E D E D
Want the effect of E on D (E precedes D) C
Observe the two associations
C-E and C-D E D
Not enough information!
Different analyses for: C C
Causal information E D E D
Confounder
Mediator
Need causal information from outside the data to do a proper analysis!
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3. Agenda Background DAG concepts Analyzing DAGs Association, Cause
Confounder, Collider
Paths
Analyzing DAGs
Examples
DAG concepts
Define a few main concepts
Paths: Surprisingly few rules needed
Analyzing DAGs
Examples: conf, intermediate, collider
Selection bias, Information bias
Rand, Mend Rand
The two former: manual for use
More on DAGs
Deeper thoughts and problems
With exercises, difficult to guess time
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4. Why causal graphs? Problem Causal graphs help:
Association measures are biased
Causal graphs help:
Understanding
Confounding, mediation, selection bias
Analysis
Adjust or not
Discussion
Precise statement of prior assumptions
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5. Causal versus casual
CONCEPTS
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6. god-DAG Causal Graph: Read of the DAG: Causality = arrows Estimations:
Node = variable
Arrow = cause
E=exposure, D=disease
DAG=Directed Acyclic Graph
Read of the DAG:
Causality = arrows
Associations = paths
Independencies = no paths
Estimations:
E-D association has two parts:
ED causal effect keep open
ECUD bias try to close
Arrows=lead to or causes
Time
E- exposure
D- disease
C, V - cofactor, variable
U- unmeasured
Directed= arrows
Acyclic = nothing can cause itself
E[C]UD Condition (adjust) to close
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7. Association and Cause Association 3 possible causal structure E D
(Reversed cause) E D
Assume E precedes D in time
Association: observe
Cause: infer (extra knowledge)
Causal structure force on the data
Basic structures, may generalize with many more variables: use paths
+ more complicated structures
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8. Confounder idea + A common cause Adjust for smoking Smoking
Yellow fingers
Smoking
Lung cancer + + +
Yellow fingers
Lung cancer +
A confounder induces an association between its effects
Conditioning on a confounder removes the association
Condition = (restrict, stratify, adjust)
Simplest form
“+” (assume monotonic effects)
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9. Collider idea or + and Two causes for selection to study
Selected subjects
Selected
Yellow fingers
Selected
Lung cancer + + +
Yellow fingers
Lung cancer or
+ and
Conditioning on a collider induces an association between its causes
“And” and “or” selection leads to different bias
Simplest form
“+” (assume monotonic effects)
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10. Data driven analysis C E D C C C E D E D E D
- Want the effect of E on D (E precedes D)
- Observe the two associations C-E and C-D
- Assume statistical criteria dictates adjusting for C
(likelihood ratio, Akaike (赤池 弘次) or 10% change in estimate) C E D
The undirected graph above is compatible with three DAGs: C C C E D E D E D
Hirotugu Akaike 赤池 弘次
Confounder
1. Adjust
Mediator
2. Direct: adjust
3. Total: not adjust
Collider
4. Not adjust
Conclusion: The data driven method is correct in 2 out of 4 situations
Need information from outside the data to do a proper analysis
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11. Paths The Path of the Righteous Feb-19 Feb-19 Feb-19 H.S. H.S. H.S. 11
Ezekiel 25:17. "The Path of the Righteous Man Is Beset on All Sides by The inequities of the Selfish and the Tyranny of Evil Men."
(Pulp Fiction version)
Paths
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12. Path definitions
Path: any trail from E to D (without repeating itself)
Type: causal, non-causal
State: open, closed
Path 1
E®D 2
E®M®D 3
E¬C®D 4
E®K¬D
Four paths:
Notice: path with or against the arrows
Paths show potential association
Goal:
Keep causal paths of interest open
Close all non-causal paths
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13. Four rules 1. Causal path: ED 2. Closed path: K
(all arrows in the same direction) otherwise non-causal
Before conditioning:
2. Closed path: K
(closed at a collider, otherwise open)
Conditioning on:
3. a non-collider closes: [M] or [C]
4. a collider opens: [K]
(or a descendant of a collider)
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14. ANALYZING DAGs
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15. Confounding examples Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 H.S.
Informal, no strict notation/def
Casual about the causal!
Confounding examples
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16. Physical activity and Coronary Heart Disease (CHD)
We want the total effect of Physical Activity on CHD. What would we adjust for?
Unconditional
Path
Type
Status 1
E®D
Causal
Open 2
E¬C1®D
Non-causal 3
E¬C2®D
This is an example
of confounding
Bias
Noncausal open=biasing path
Conditioning on C1 and C2
Path
Type
Status 1
E®D
Causal
Open 2
E¬[C1]®D
Non-causal
Closed 3
E¬[C2]®D
No bias
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17. Intermediate variables
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18. Tea and depression
Total effect: Direct effect: Caffeine intermediate or confounder?
adjust for O
adjust for C (and O)
Caffeine is both intermediate and part of a confounder path.
Path
Type
Status 1
E→D
Causal
Open 2
E→C→D 3
E←O→C→D
Non-causal
Tea and depression: Finnish study
Caffeine reduces depression: Nurses Health Study
direct
total
indirect
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19. Statin and CHD
We 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)?
Nothing
No, U is unmeasured
No adjustments gives
the total effect
Adjusting for C will close path 2
but will open path 3 and give bias!
C is a collider on path 3
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20. Selection bias Two concepts Feb-19 Feb-19 Feb-19 Feb-19 Feb-19 Feb-19
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21. Convenience sample, homogenous sample
hospital
Convenience sample:
Conduct the study among
hospital patients? E
diabetes D
fractures
2. Homogeneous sample:
Population data,
exclude hospital patients?
Conditional
Path
Type
Status 1
E→D
Causal
Open 2
E→[H]←D
Non-Causal
Unconditional
Path
Type
Status 1
E→D
Causal
Open 2
E→H←D
Non-causal
Closed
Collider, selection bias
Collider stratification bias: at least on stratum is biased
This type of selection bias can be adjusted for!
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22. Summing up Better discussion based on DAGs Draw your assumptions
Data driven analyses do not work. Need (causal) information from outside the data.
DAGs are intuitive and accurate tools to display that information.
Paths show the flow of causality and of bias and guide the analysis.
DAGs clarify concepts like confounding and selection bias, and show that we can adjust for both.
Better discussion based on DAGs
Draw your assumptions
before your conclusions
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23. Recommended reading Books Papers
Hernan, M. A. and J. Robins. Causal Inference. Web:
Rothman, K. J., S. Greenland, and T. L. Lash. Modern Epidemiology, 2008.
Morgan and Winship, Counterfactuals and Causal Inference, 2009
Pearl J, Causality – Models, Reasoning and Inference, 2009
Veierød, M.B., Lydersen, S. Laake,P. Medical Statistics. 2012
Papers
Greenland, S., J. Pearl, and J. M. Robins. Causal diagrams for epidemiologic research, Epidemiology 1999
Hernandez-Diaz, S., E. F. Schisterman, and M. A. Hernan. The birth weight "paradox" uncovered? Am J Epidemiol 2006
Hernan, M. A., S. Hernandez-Diaz, and J. M. Robins. A structural approach to selection bias, Epidemiology 2004
Berk, R.A. An introduction to selection bias in sociological data, Am Soc R 1983
Greenland, S. and B. Brumback. An overview of relations among causal modeling methods, Int J Epidemiol 2002
Weinberg, C. R. Can DAGs clarify effect modification? Epidemiology 2007
Hernan and Robins Causal inference (web)
Hernan a struct approach
Hernandez- From causal
Shahar
Rothman
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