October 15H.S.1 Causal inference Hein Stigum Presentation, data and programs at: .
Apr-15H.S.1 Simple Causal Graphs Hein Stigum Presentation, data and programs at: Simple Casual...
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Transcript of Apr-15H.S.1 Simple Causal Graphs Hein Stigum Presentation, data and programs at: Simple Casual...
04/21/23 H.S. 1
Simple Causal Graphs
Hein Stigum
Presentation, data and programs at:
http://folk.uio.no/heins/
Simple Casual Graphs
04/21/23 H.S. 2
Causal graphs
• 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
04/21/23 H.S. 3
Exposure-Disease influenced by C
• C can be:– Confounder
– Intermediate (in 2. Path)
– Collider
– Effect modifier
• Use graphs– Determine C-type
– Choose analysis
E D
C
04/21/23 H.S. 4
Example
• Exposure– Pysical Activity: PA
• Disease– Diabetes type 2: D2
• Covariates– Smoking: S
– Health Conscious: HC
– Overweight: Ov
– Blood Pressure: BP
04/21/23 H.S. 5
Linear models
• 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.
0Diabetes type 2
mod 1 mod 2 mod 3 mod 4Pysical Activity -3 pp -2 pp -1.5 pp -0.5 ppSmokingOverweightBlood Pressure
04/21/23 H.S. 6
No influence of C
E D
C
E D
C
E D
C
04/21/23 H.S. 7
Confounder: Smoking
• Should adjust for Smoking– Stratify
– Regression
D2 PA
S
+-
0
biased true
Negative bias
-2-3
04/21/23 H.S. 8
Confounder 2
Adjust for Smoking or
for Health Consciousness
Assume all following models are adjusted for smoking
D2 PA
SNegative bias
HC
+
-
+
0
biased true
-2-3
04/21/23 H.S. 9
Intermediate (in 2. path): Overweight
Alt 1: Ignore OverweightTotal -2.0D2 PA
Ov
+-
PA
Ov Alt 2: Two models:Direct c2 -1.5
Indirect b1*c1 -0.5
Total c2+ b1*c1 -2.0D2 PA
Ov
c2
b1 c1
Simply adjusting for Overweight is not OK!
04/21/23 H.S. 10
Collider idea
• Conditioning on a collider induces an association between the causes
• Condition = (restrict, stratify, adjust)• Bias direction?
Hip arthritis
Limp
Knee injury
Two causes for limping
-
++
Hip arthritis
Limp
Knee injury
Select limping subjects
++
04/21/23 H.S. 11
Collider: Blood Pressure
• Should not adjust for Blood Pressure
• Problem if selection is connected to BP
D2 PA
BP
+-
0
biasedtrue
Positive bias if we adjust
04/21/23 H.S. 12
Best model (so far)
• Model 2 is best
• Used extra info in graphs to decide
Diabetes type 2mod 1 mod 2 mod 3 mod 4
Pysical Activity -3 pp -2 pp -1.5 pp -0.5 ppSmoking ConfounderOverweight IntermediateBlood Pressure Collider
04/21/23 H.S. 13
Effect modifier: Sex
• Alt 2: Model with interaction– Technical
– Test for interaction
– Efficient (7 estimates)
D2 PA
Sex
• Alt 1 : Two models– Easy
– No test for interaction
– Inefficient (12 estimates)
Two modelsMales Females
PA -2.5 -1.5Co 1Co 2Co 3Co 4const
Model with interactionMales Females
PA -2.5 -1.5Co 1Co 2Co 3Co 4const
• Alt 3 : Ignore Sex
04/21/23 H.S. 14
Effect modifier: SexModel with interaction term
• Test for interaction– Wald test on b3=0
• If significant interaction– Sex is coded 0 for Males and 1 for Females
– The effect of PA (1 unit increase)
...2 3210 SexPAbSexbPAbbD
31
1
:Femalesfor
:Malesfor
bb
b
• Linear model
-2.5
-1.5
04/21/23 H.S. 15
Examples
04/21/23 H.S. 16
Smoking and LRTIThe truth is out there?
LRTI Smoke
Educ
--
S
LRTI=Lower Resperatory Tract InfectionsWant: effect of smoking in pregnancy on LRTI in childrenHave: 40% response, high education is overrepresented
Best causal estimate:Crude smoke-LRTI under 100% response?Crude smoke-LRTI under 40% response?
Education is a confounderSelection represents partial adjustment
04/21/23 H.S. 17
Smoking and LRTI, ex 2
LRTI Smoke
Educ S
• 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
04/21/23 H.S. 18
Ethnicity and lung function
• Exposure Ethnic group• Outcome Lung function• Covariates Hemoglobin, height
• Draw DAG• Suggest analyzes/models• Model with all covariates meaningful?
Lung func Hemo
HeightEthnic
04/21/23 H.S. 19
ModelsModel 1
Lung func Ethnic
Model 2
Lung func Hemo
Height
Lung func Hemo
HeightEthnic
Hart rate
Model 3 Model 4
Lung func Hemo
Height
Ethnic
04/21/23 H.S. 20
Summing up
• 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