1. Hein Stigum http://folk.uio.no/heins/ courses
DAGs intro, Answers
Hein Stigum
courses
28. nov.
H.S.

2. Report variables as equals?
Comments (surprises)
Diabetes 2
2.0
Physical activity
1.2
Protective in other studies?
Obesity
1.0
No effect?
Bone density
0.8
P is a confounder for E→D, but is E a confounder for P→D?
No, E is in the causal path P→ E→ D
Which effects are reported correctly in the table?
physical activity P
Only the effects of E and B!
P has indirect effect
P→ E→ D
O has indirect effects
O→ E→ D and O→ B→ D
diabetes 2 E
fractures D
obesity O
bone density B
DAGs dictate one exposure and one outcome
Report adjusted effect of exposure
Nov-18
H.S.

3. Stratified analysis (Simpson’s paradox)C C
P=0.16
Re=2.0
Rd=5.0
Red=0.6
Low Bp=30% A D A D
C is a collider, not stratify,
RR=1.4
C is a confounder, stratify,
RR=0.6
C could also be a mediator, RR=?
Nov-18
H.S.

4. Physical activity and Coronary Heart Disease (CHD)
Total effect: adjust for sex and age
Unconditional
Path
Type
Status 1
E®D
Causal
Open 2
E¬C1®D
Non-causal 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
Non-causal
Closed 3
E¬[C2]®D
What if sex does not
affect physical activity?
No bias
Nov-18
Nov-18
Nov-18
H.S.
H.S. 4 4

5. Tea and depression Paths Total effect: adjust for O
Direct effect: 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
Natural direct effects: Lange, T. , Vanstelandt, Vanderweele
direct
total
indirect
Questions:
Coffee → tea or tea → coffee?
Controlled direct effect!
Nov-18
H.S.

6. Statin and CHD Paths: Total effect: no adjustments
Direct effect: not possible
C intermediate or collider: intermediate (path 2) and collider (path 3)
Randomizing statin treatments ensures same lifestyle in both groups,
But conditioning on C induces bias anyway.
Subgroup analyses: look at effect of statin->CHD for high or low cholesterol. Partial conditioning on C.
no bias
Questions:
RandomizedControlledTrial?
Subgroup analyses?
bias!
Nov-18
H.S.

7. Survival bias Conclusion: Have survival bias
risk
Paths:
ED Causal Open
E[S]RD Non-causal Open E
early exposure D
later disease
E and R are unrelated causes for disease
Conclusion:
Have survival bias
Must adjust for R to remove the bias
28. nov.
H.S.

8. Survival bias Conclusion: Have survival bias
Paths:
ED Causal Open
E[S]RD Non-causal Open
Early%20exposure E @0.0,0.5
Later%20disease O @1.0,0.5
Risk 1 @1.0,0.4
Survival A @0.3,0.4
Early%20exposure Later%20disease Survival
Risk Later%20disease Survival
E and R are unrelated causes for disease
Conclusion:
Have survival bias
Must adjust for R to remove the bias
28. nov.
H.S.

9. RCT c IVe ITTe 𝐼𝑉= 𝐼𝑇𝑇 𝑐 = −0.2 0.85 =−0.24 Negative bias
-0.15
0.22
𝐼𝑉= 𝐼𝑇𝑇 𝑐 = − =−0.24
U->E -
U->D - -*- = positive bias
Do not have the information of U
Bias=crude-true=PP - IV=0.1=a*b*var(U)/var(E)
If the variances are about the same then a*b=0.1
Negative bias
from confounding
ITT always “weaker” than IV
28. nov.
H.S.

10. Exercise: causal pies Sufficient causes for Hospital: Selection bias:
Causal pies for hospital
Selection bias:
Sufficient causes for Hospital:
1) or
2) and
3) both
Selection bias:
Negative bias
Positive bias ?
Question
Variable with only 1 value?
Nov-18
H.S.

11. Dust and COPD Paths: Total effect: no adjustments
Direct effect: not possible
C intermediate or collider: intermediate (path 2) and collider (path 3)
Randomizing statin treatments ensures same lifestyle in both groups,
But conditioning on C induces bias anyway.
Subgroup analyses: look at effect of statin->CHD for high or low cholesterol. Partial conditioning on C.
no bias
Questions:
RandomicedControlledTrial?
Subgroup analyses?
bias!
Nov-18
H.S.

12. 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
1. Paths: (No adjusting)
ED Causal Open
EACBD Non-causal Closed No bias
2. Paths: (Conditioning on C)
ED Causal Open
EA[C]BD Non-causal Open bias A B
3. We are conditioning on a collider,
hence: selection bias! C E D
28. nov.
Nov-18
Nov-18
H.S.
H.S. 12 12

13. Exercise: Collider stratification
Hospital risk:
Selection bias
Collider stratification bias
Nov-18
H.S.

14. Oestrogen and endometrial cancer
Paths from E (oestrogen) to C (cancer)
Unconditional
Path
Type
Status 1
E®B®A¬C
Non-causal
Closed 2
E®B¬C
No bias
Conditioning on B
Path
Type
Status 1
E®[B]®A¬C
Non-causal
Closed 2
E®[B]¬C
Open
collider bias

15. Confounding between mediator and outcome
Paths from X to Y:
Unconditional
Path
Type
Status 1
X®Y
Causal
Open 2
X®Z®Y 3
X®Z¬U®Y
Non-causal
Closed
total effect
Conditioning on Z
Path
Type
Status 1
X®Y
Causal
Open 2
X®[Z]®Y
Closed 3
X®[Z]¬U®Y
Non-causal
direct effect
collider bias

16. Dust and lung disease Selection bias (collider stratification)
C.worker C
health
Paths:
ED Causal Open
E[S]CD Non-causal Open
Selection bias (collider stratification)
Healthy worker effect, can show protective effects
Selection bias (interaction based)
Good health: RRED = 2.0
Bad health: RRED = 3.0
Can not show protective effect E
dust D
lung disease S
C.worker C
health
Cross-sectional study: dust sensitive change work, health common to work status and (less) lung disease
No confounding: for simplicity (1 and 3) or randomization (2)
Major selection biases: all have the collider structure!
All cases could be adjusted to remove selection bias
The effect found among the workers is not true!
Interaction
Nov-18
H.S.

17. Dust and lung disease Selection bias (collider stratification)
C.worker C
health
Selection bias (collider stratification)
Healthy worker effect, can show protective effect
Can show untrue effects
Adjust for health to remove bias
Selection bias (interaction based)
Good health: RRED = 1.0
Bad health: RRED = 2.0
Can not show protective effect
The E-D arrow is not required
Can only show “true effects” E
dust D
lung disease S
C.worker C
health
Cross-sectional study: dust sensitive change work, health common to work status and (less) lung disease
No confounding: for simplicity (1 and 3) or randomization (2)
Major selection biases: all have the collider structure!
All cases could be adjusted to remove selection bias
The effect found among the workers is not true!
Interaction
Nov-18
H.S.

18. Exercise: Simpson’s paradox
Want the effect of treatment (T) on disease (D)
Both T and D affect blood pressure (Bp) Bp
Draw the DAG
Calculate the population effect of T on D
Conclusions? T D
Population
Low blood pressure
High blood pressure
Selection forces (for high Bp):
P=0.84, Rd=0.26, Rt=0.78, Rtd=0.42
Unbiased
Collider bias
Collider bias
Nov-18
H.S.

19. Exercise: Dust and COPD Chronic Obstructive Pulmonary Disease
cur. worker D0
diseases H
health
COPD risks: E0
prior dust E
cur. dust D
COPD
No interaction, can we still have selection bias?
Paths:
ED Causal Open
E E0D0[S]HD Non-causal Open
COPD: Chronic obstructive pulmonary disease
Risk factors: smoking, air pollution, genetics, workplace dust
Crude RR=0.7. Adjust for H, Health: True RR=2.
Healthy worker bias (selection bias concept 2)
No interaction based selection bias, no interaction (on RR scale, but on the RD).
Nov-18
H.S.

20. Exercise: nested counterfactuals
A set to 1, M set to m D1,m
A set to 0, M set to m D0,m
A set to 1, M set to M0 D1,M0
A set to 0, M set to M0 D0,M0
Nov-18
H.S.

21. Exercise: Labor marked discrimination
Describe the experiment for estimating the controlled direct effect:
Draw names, use standard CV
Describe the experiment for estimating the natural direct effect:
Draw names, draw CV from sample of “white CVs” (assuming white is “untreated”) CV
name
Job
Nov-18
H.S.

22. Hair dye and congenital malformations
Reported dye
E as exposure
Path
Type
Status 1
E®D
Causal
Open 2
E®E*¬D
Non-causal
Closed ?
No bias + E
True dye D
malformation +
E* as exposure
Path
Type
Status 1
E*¬E®D
Non-causal
Open 2
E*¬D
Bias, but
True E*
Bias from E
4) Yes
28. nov.
H.S.