DAGs intro, Answers
Hein Stigum
http://folk.uio.no/heins/
courses
29. mai.
H.S.
1
Report variables as equals?
Variable
OR
Comments (surprises)
Diabetes 2
2.0
Physical activity
1.2
Protective in other studies?
Obesity
1.0
No effect?
Bone density
0.8
1. 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
2. Which effects are reported correctly
in the table?
P
physical activity
E
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
D
fractures
diabetes 2
O
B
obesity
bone density
DAGs dictate one exposure and one outcome
Report adjusted effect of exposure
May-16
H.S.
2
Stratified analysis (Simpson’s paradox)
Population
D
A
1
0
C=0
D
1
0
sum
210
150
290
350
500
500
1000
RR=
1.4
40% more disease if treated
risk
0.4
0.3
A
1
0
C=1
D
1
0
sum
risk
10
70
90
330
100
400
500
0.10
0.18
RR=
0.6
40% less disease if treated
C
A
1
A0
1
0
sum
risk
200
80
200
20
400
100
500
0.50
0.80
RR=
0.6
40% less disease if treated
C
D
A
C is a collider,
not stratify,
RR=1.4
D
C is a confounder,
stratify,
RR=0.6
C could also be a mediator, RR=?
May-16
H.S.
3
Physical activity and
Coronary Heart Disease (CHD)
1. Total effect: adjust for sex and age
Unconditional
Path
1 ED
2 EC1D
3 EC2D
Conditioning on C1
and C2
Path
1 ED
2 EC1]D
3 EC2]D
May-16
Type
Causal
Non-causal
Non-causal
Status
Open
Open
Open
Bias
What if sex does not
affect physical activity?
Type
Causal
Non-causal
Non-causal
Status
Open
Closed
Closed
H.S.
No bias
4
Tea and depression
O
coffee
1. Paths
C
2. Total effect: adjust for O
caffeine
3. Direct effect: adjust for C (and O)
E
tea
Path
1 E→D
2 E→C→D
3 E←O→C→D
D
depression
Type
Status
Causal
Open
Causal
Open
Non-causal Open
4. Caffeine is both intermediate and
part of a confounder path.
direct
indirect
total
Questions:
Coffee → tea or tea → coffee?
Controlled direct effect!
May-16
H.S.
5
Statin and CHD
1.
2.
3.
4.
Paths:
Total effect: no adjustments
Direct effect: not possible
C intermediate or collider: intermediate (path 2)
and collider (path 3)
Unconditional
Path
1 ED
2 ECD
3 ECUD
Type
Causal
Causal
Non-causal
Status
Open
Open
Closed
Conditioning on C
Path
1 ED
2 EC]D
3 EC]UD
Type
Causal
Causal
Non-causal
Status
Open
Closed
Open
May-16
H.S.
no bias
bias!
Questions:
RandomizedControlledTrial?
Subgroup analyses?
6
Exercise: nested counterfactuals
1. A set to 1, M set to m
D1,m
2. A set to 0, M set to m
D0,m
3. A set to 1, M set to M0
D1,M0
4. A set to 0, M set to M0
D0,M0
May-16
H.S.
7
Exercise: Labor marked discrimination
1. Describe the experiment for estimating
the controlled direct effect:
–
Draw names, use standard CV
2. Describe the experiment for estimating
the natural direct effect:
–
CV
Job
name
Draw names, draw CV from sample of “white
CVs” (assuming white is “untreated”)
May-16
H.S.
8
Hair dye and congenital malformations
E*
Reported dye
?
+
E
+
True dye
D
malformation
E as exposure
Path
1 ED
2 EE*D
Type
Status
Causal
Open
Non-causal Closed
E* as exposure
Path
1 E*ED
2 E*D
Type
Status
Non-causal Open
Non-causal Open
True E*
No bias
Bias, but
Bias from E
4) Yes
0
29. mai.
H.S.
9
Survival bias
S
R
survival
risk
E
D
early exposure
later disease
Paths:
ED
Causal
E[S]RD Non-causal
Open
Open
Conclusion:
Have survival bias
Must adjust for R to remove the bias
29. mai.
H.S.
10
U
RCT
E
R
+
-
+
85
0
85
15
100
115
D
R
+
-
+
43
63
106
57
37
94
D
E
+
-
+
32
74
106
53
41
94
N
Risk
RD
100
100
200
0.85
0.00
0.85
0
N
Risk
RD
100
100
0.43
0.63
-0.20
0
N
Risk
RD
85
115
0.38
0.64
-0.27
0
R c E
c compliance
0.22
D
IVe
ITTe
𝐼𝑉 =
Negative bias
from confounding
29. mai.
-0.15
𝐼𝑇𝑇
𝑐
=
−0.2
0.85
= −0.24
ITT ITT effect
PP PP effect
ITT always “weaker” than IV
H.S.
11
Exercise: causal pies
1. Causal pies for hospital
2. Selection bias:
Sufficient causes for Hospital:
1) or
2) and
3) both
Selection bias:
Question
Variable with only 1 value?
May-16
1)
2)
3)
H.S.
Negative bias
Positive bias
?
12
Exercise: Dust and COPD
Chronic Obstructive Pulmonary Disease
D0
S
cur. worker
diseases
H
health
COPD risks:
Health
E0
prior dust
E
cur. dust
good
poor
Dust
low
high
5 % 10 %
10 % 20 %
RRdust RDdust
2.00 5 %
2.00 10 %
D
COPD
1. No interaction, can we still have selection bias?
2. Paths:
ED
E E0D0[S]HD
Causal
Non-causal
Open
Open
3. Crude RR=0.7. Adjust for H, Health: True RR=2.
4. Healthy worker bias (selection bias concept 2)
5. No interaction based selection bias, no interaction (on RR scale, but on the RD).
May-16
H.S.
13
Dust and COPD
1.
2.
3.
4.
Paths:
Total effect: no adjustments
Direct effect: not possible
C intermediate or collider: intermediate (path 2)
and collider (path 3)
Unconditional
Path
1 ED
2 ECD
3 ECUD
Type
Causal
Causal
Non-causal
Status
Open
Open
Closed
Conditioning on C
Path
1 ED
2 EC]D
3 EC]UD
Type
Causal
Causal
Non-causal
Status
Open
Closed
Open
May-16
H.S.
no bias
bias!
Questions:
RandomicedControlledTrial?
Subgroup analyses?
14
Exercise: M-structure
A
B
C
E
D
A
B
C
E
1. Show the paths
2. Should we adjust for C?
3. If the design implies a selection on C, what would you
call the resulting bias: selection bias or confounding?
1. Paths: (No adjusting)
ED
Causal
EACBD
Non-causal
Open
Closed No bias
2. Paths: (Conditioning on C)
ED
Causal
EA[C]BD
Non-causal
Open
Open
bias
3. We are conditioning on a collider,
hence: selection bias!
D
29. mai.
May-16
H.S.
15
Exercise: Collider stratification
H
Hospital risk:
D
1
E
0
2.0
1
0
0.6
0.3
0.2
0.1
Response=
16 %
Population
D
E
1
0
0
sum
36
164
64
736
100
900
1000
RR=
2.0
May-16
E
Hospital
D
1
E
3.0
1
0
D
2.0
No hospital
D
1
0
sum
22
49
13
74
35
123
157
RR=
1.6
E
1
0
1
0
sum
15
115
51
663
65
777
843
RR=
1.5
Selection bias
H.S. Collider stratification bias
16
Oestrogen and endometrial cancer
Paths from E (oestrogen) to C (cancer)
Unconditional
Path
1 EBAC
2 EBC
Type
Status
Non-causal Closed
Non-causal Closed
Conditioning on B
Path
Type
Status
1 E[B]AC Non-causal Closed
2 E[B]C
Non-causal Open
No bias
collider bias
Confounding between mediator and outcome
Paths from X to Y:
Unconditional
Path
1 XY
2 XZY
3 XZUY
Type
Causal
Causal
Non-causal
Status
Open
Open
Closed
Conditioning on Z
Path
1 XY
2 XZ]Y
3 XZ]UY
Type
Causal
Causal
Non-causal
Status
Open
Closed
Open
total effect
direct effect
collider bias
Dust and lung disease
S
C
C.worker
health
E
D
dust
lung disease
Paths:
ED
Causal
E[S]CD Non-causal
Open
Open
• Selection bias (collider stratification)
• Healthy worker effect, can show protective effects
S
C
C.worker
health
E
D
dust
lung disease
May-16
• Selection bias (interaction based)
Good health:
Bad health:
RRED = 2.0
RRED = 3.0
Interaction
• Can not show protective effect
H.S.
19
Dust and lung disease
S
C
C.worker
health
E
D
dust
lung disease
• Selection bias (collider stratification)
• Healthy worker effect, can show protective
effect
• Can show untrue effects
• Adjust for health to remove bias
S
C
C.worker
health
E
D
dust
lung disease
May-16
• Selection bias (interaction based)
Good health:
Bad health:
RRED = 1.0
RRED = 2.0
Interaction
• Can not show protective effect
•
The E-D arrow is not required
•
Can only show “true effects”
H.S.
20
Exercise: Simpson’s paradox
Want the effect of treatment (T) on disease (D)
Both T and D affect blood pressure (Bp)
1. Draw the DAG
2. Calculate the population effect of T on D
3. Conclusions?
Bp
T
D
Population
D
T
1
0
Low blood pressure
D
1
0
sum
70
230
130
570
200
800
1000
RR=
1.2
risk
0.4
0.3
20% more disease if treated
Unbiased
May-16
T
1
0
1
0
sum
risk
65
180
45
90
110
270
380
0.6
0.7
RR=
0.9
10% less disease if treated
Collider bias
H.S.
High blood pressure
D
T
1
0
1
0
sum
risk
5
50
85
480
90
530
620
0.06
0.09
RR=
0.6
40% less disease if treated
Collider bias
21