Apr-20
Simple Casual Graphs
Hein Stigum
Presentation, data and programs at: http://folk.uio.no/heins/
H.S.
1

• Simple causal graphs
– Proper analysis (adjust or not)
– Direction of bias
• Directed Acyclic Graphs (DAGs)
– Formal tool
– Inventory of variables
– Proper analysis (adjust or not)
– Causal inference
Apr-20 H.S.
2

E
Apr-20
C
Exposure-Disease influenced by C
D
• C can be:
– Confounder
– Intermediate (in 2. Path)
– Collider
– Effect modifier
• Use graphs
– Determine C-type
– Choose analysis
H.S.
3

• Exposure
– Pysical Activity: PA
• Disease
– Diabetes type 2: D2
• Covariates
– Smoking: S
– Health Conscious: HC
– Overweight: Ov
– Blood Pressure: BP
Apr-20 H.S.
4

0
Diabetes type 2
Pysical Activity
Smoking
Overweight
Blood Pressure mod 1
-3 pp mod 2
-2 pp mod 3
-1.5 pp mod 4
-0.5 pp
• Best model?
– Likelihood ratio tests or Akaike criteria  mod 4
– All changes in PA effect considered important  mod 4
– Claim mod 2.
• Model choice can not be based on data only.
• Need extra info or assumptions.
Apr-20 H.S.
5

E
Apr-20
C
D
C
E
H.S.
D
C
E
6
D

PA
-
S
+
D2
Negative bias biased true
-3 -2 0
• Should adjust for Smoking
– Stratify
– Regression
Apr-20 H.S.
7

HC
-
+
PA
S
+
D2
Negative bias biased true
-3 -2
Adjust for Smoking or for Health Consciousness
0
Assume all following models are adjusted for smoking
Apr-20 H.S.
8

PA
Ov
+
D2
Alt 1: Ignore Overweight
Total -2.0
PA b1
Ov
PA
Ov c2 c1
D2
Alt 2: Two models:
Direct c2
Indirect b1*c1
-1.5
-0.5
Total c2+ b1*c1 -2.0
Simply adjusting for Overweight is not OK!
Apr-20 H.S.
9

Two causes for limping
Limp
Select limping subjects
Limp
+ + + +
Hip arthritis Knee injury Hip arthritis Knee injury
-
• Conditioning on a collider induces an association between the causes
• Condition = (restrict, stratify, adjust)
• Bias direction?
Apr-20 H.S.
10

PA
-
BP
+
D2
Positive bias if we adjust true biased
0
• Should not adjust for Blood Pressure
• Problem if selection is connected to BP
Apr-20 H.S.
11

Diabetes type 2
Pysical Activity
Smoking
Overweight
Confounder
Intermediate
Blood Pressure Collider mod 1
-3 pp mod 2
-2 pp mod 3
-1.5 pp mod 4
-0.5 pp
• Model 2 is best
• Used extra info in graphs to decide
Apr-20 H.S.
12

Sex
PA
Two models
Males
PA
Co 1
-2.5
Co 2
Co 3
Co 4 const
D2
Females
-1.5
Model with interaction
Males Females
PA
Co 1
-2.5
-1.5
Co 2
Co 3
Co 4 const
Apr-20
• Alt 3 : Ignore Sex
• Alt 1 : Two models
– Easy
– No test for interaction
– Inefficient (12 estimates)
• Alt 2: Model with interaction
– Technical
– Test for interaction
– Efficient (7 estimates)
H.S.
13

Effect modifier: Sex
Model with interaction term
• Linear model
D 2
 b
0
 b
1
PA
 b
2
Sex
 b
3
PA

Sex

...
• Test for interaction
– Wald test on b
3
=0
• If significant interaction
– Sex is coded 0 for Males and 1 for Females
– The effect of PA (1 unit increase)
-2.5
for for
Males : b
1
Females : b
1
 b
3
-1.5
Apr-20 H.S.
14

Apr-20
Examples
H.S.
15

The truth is out there?
LRTI= Lower Resperatory Tract Infections
Want: effect of smoking in pregnancy on LRTI in children
Have: 40% response , high education is overrepresented
Best causal estimate:
Crude smoke-LRTI under 100% response?
Crude smoke-LRTI under 40% response?
Smoke
-
Educ
-
S
LRTI
Apr-20 H.S.
Education is a confounder
Selection represents partial adjustment
16

Educ
S
Smoke LRTI
• Education is a not a confounder
• Crude smoke-LRTI in population is unbiased
• Crude smoke-LRTI in sample is biased, S is a collider
• Adjusted smoke-LRTI in sample is unbiased
Apr-20 H.S.
17

• Exposure
• Outcome
• Covariates
Ethnic group
Lung function
Hemoglobin, height
• Draw DAG
• Suggest analyzes/models
• Model with all covariates meaningful?
Ethnic Height
Hemo Lung func
H.S.
Apr-20 18

Ethnic
Model 1
Lung func
Hemo
Model 2
Height
Lung func
Model 3
Ethnic Height
Hemo
Model 4
Height
Lung func
Hemo
Hart rate
Apr-20
Lung func
H.S.
Ethnic
19

• In a study of 2 variables, a 3 . variable may have 4 effects:
Confounder, Intermediate, Collider, Effect modifier
• Not distinguished from data, need extra info
• Casual graphs help use the extra info
Apr-20 H.S.
20