1. Causal Graphs, epi forum
Endringer:
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Ta ut vitamin eks., kan også hoppe over konfounding def.
Hein Stigum
talks
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2. Agenda Motivating examples Concepts Analyzing DAGs Examples
Confounder, Collider
Analyzing DAGs
Paths
Examples
Confounding
Mixed (confounders and mediators)
Selection bias
Define a few main concepts
More as we go along
Surprisingly few needed
With exercises, difficult to guess time
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3. Why causal graphs? Problem Understanding Analysis Discussion
Association measures are biased
Understanding
Confounding, selection bias, mediators
Analysis
Adjust or not
Discussion
Precise statement of prior assumptions
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4. Motivating examples Statins and coronary heart disease
Disease risk: lifestyle, cholesterol
Diabetes and fractures
Disease risk: fall, bone density
Exposure risk: BMI, Physical activity
Analyze among hospital patients
Exclude hospital patients
Adjust
or not?
Exclude
or not?
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5. Concepts Causal versus casual Apr-17 Apr-17 Apr-17 Apr-17 Apr-17
Informal, no strict notation/def
Casual about the causal!
Concepts
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6. DAG=Directed Acyclic Graph
god-DAG
DAG=Directed Acyclic Graph C
age U
obesity
Node = variable
Arrow = cause, (at least one individual effect) E
vitamin D
birth defects
Arrows=lead to or causes
Time
E- exposure
D- disease
C, V - cofactor, variable
U- unmeasured
Directed= arrows
Acyclic = nothing can cause itself
Read of the DAG:
Causality = arrows
Associations = paths
Questions on the DAG:
E-D effect biased?
Adjust for age?
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7. Possible causal structure
Association and Cause
Association
Possible causal structure
Lung
cancer
Yellow
fingers
Cause
Lung
cancer
Yellow
fingers
Confounder
Smoke
Yellow
fingers
Lung
cancer
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
Lung
cancer
Yellow
fingers
Collider
Hospital
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8. Confounder idea + A common cause Adjust for smoking Yellow fingers
Lung cancer +
Smoking + +
Yellow fingers
Lung cancer +
A confounder induces an association between its effects
Conditioning on a confounder removes the association
Condition = (restrict, stratify, adjust)
“+” (assume monotonic effects)
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9. Collider idea or + and Two causes for coming to hospital
Yellow fingers
Hospital
Lung cancer
Select subjects in hospital +
Hospital + +
Yellow fingers
Lung cancer or
+ and
Conditioning on a collider induces an association between its causes
“And” and “or” selection leads to different bias
“+” (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 E-C and D-C
Assume criteria dictates adjusting for C
(likelihood ratio, Akaike (赤池 弘次) or 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. Adjust (direct)
3. Not adjust (total)
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. Analyzing DAGS: Paths The Path of the Righteous Apr-17 Apr-17 Apr-17
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)
Analyzing DAGS: Paths
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12. Path definitions
Path: any trail from E to D (without repeating or crossing itself)
Type: causal, non-causal
State: open, closed K
Path 1
E®D 2
E®M®D 3
E¬C®D 4
E®C¬D C
Four paths: E D M
Goal:
Keep causal paths of interest open
Close all non causal paths
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13. Four rules K C 1. Causal path: ED E D M K 2. Closed path: K C E D
non-causal C
1. Causal path: ED
(all arrows in the same direction) otherwise non-causal E D
causal M K
closed
Before conditioning:
2. Closed path: K
(closed at a collider, otherwise open) C E D
open M K
Conditioning on:
3. a non-collider closes: [M] or [C]
4. a collider opens: [K]
(or a descendant of a collider) C E D M
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14. Confounding Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S. H.S.
Informal, no strict notation/def
Casual about the causal!
Confounding
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15. Physical activity and Coronary Heart Disease (CHD)
age
We want the total effect of Physical Activity on CHD. What should we adjust for? E
Phys. Act. D
CHD C2
sex
Unconditional
Path
Type
Status 1
E®D
Causal
Open 2
E¬C1®D
Noncausal 3
E¬C2®D
Bias
Noncausal open=biasing path
Conditioning on C1 and C2
Path
Type
Status 1
E®D
Causal
Open 2
E¬[C1]®D
Noncausal
Closed 3
E¬[C2]®D
No bias
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16. Vitamin and birth defects
Bias in E-D?
Adjust for C? C
age U
obesity E
vitamin D
birth defects
Unconditional
Path
Type
Status 1
E®D
Causal
Open 2
E¬C®U®D
Non-causal
Bias
Noncausal open=biasing path
Both C and U are confounders
Problem that we have ”forgotten” arrow C->D?
Conditioning on C
Path
Type
Status 1
E®D
Causal
Open 2
E¬[C]®U®D
Non-causal
Closed
No bias
This example
and previous slide
are both confounding
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17. Mixed Confounders and mediators Apr-17 Apr-17 Apr-17 Apr-17 Apr-17
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18. Diabetes and Fractures
prone to fall
We want the total effect of
diabetes on fractures V
BMI E
diabetes D
fracture P
physical activity B
bone
density
Conditional
Path
Type
Status 1
E→D
Causal
Open 2
E→F→D 3
E→B→D 4
E←[V]→B→D
Non-causal
Closed 5
E←[P]→B→D
Unconditional
Path
Type
Status 1
E→D
Causal
Open 2
E→F→D 3
E→B→D 4
E←V→B→D
Non-causal 5
E←P→B→D
Mediators
Confounders
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19. Statin and CHD U
lifestyle
We want the total effect of statin on CHD. What would we adjust for?
Can we estimate the direct effect of statin on CHD (not mediated through cholesterol)? C
cholesterol E
statin D
CHD
No adjustments gives
the total effect
Mixed because C is both a mediator and a collider
Is C a collider?
Adjusting for C opens the collider path
must also adjust for U
to get the direct effect
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20. Selection bias Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 Apr-17 H.S. H.S.20 20 20 20 20 20

21. Diabetes and Fractures
Convenience:
Conduct the study among
hospital patients? H
hospital E
diabetes D
fracture
2. Homogeneous sample:
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
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22. Selection bias: size and direction
Hospital risk:
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23. Adjusting for selection bias
prone to fall H
hospital E
diabetes D
fracture
Path
Type
Status 1
E→D
Causal
Open 2
E→F→[H] ←D
Non-causal
Adjust for F to close this path
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24. Better discussion based on DAGs
Summing up
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
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25. References Hernan and Robins, Causal Inference (coming)
1 Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3. ed. Philadelphia: Lippincott Willams & Williams,2008.
Hernan MA, Hernandez-Diaz S, Robins JM. A structural approach to selection bias. Epidemiology 2004; 15:
Hernandez-Diaz S, Schisterman EF, Hernan MA. The birth weight "paradox" uncovered? Am J Epidemiol 2006; 164:
4 Schisterman EF, Cole SR, Platt RW. Overadjustment Bias and Unnecessary Adjustment in Epidemiologic Studies. Epidemiology 2009; 20:
5 VanderWeele TJ, Hernan MA, Robins JM. Causal directed acyclic graphs and the direction of unmeasured confounding bias. Epidemiology 2008; 19:
6 VanderWeele TJ, Robins JM. Four types of effect modification - A classification based on directed acyclic graphs. Epidemiology 2007; 18:
7 Weinberg CR. Can DAGs clarify effect modification? Epidemiology 2007; 18:
Hernan and Robins, Causal Inference (coming)
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