1. Presentation, data and programs at:
Simple Causal Graphs
Simple Casual Graphs
Hein Stigum
Presentation, data and programs at:
Apr-17
H.S.

2. Causal graphs Simple causal graphs Directed Acyclic Graphs (DAGs)
Proper analysis (adjust or not)
Direction of bias
Directed Acyclic Graphs (DAGs)
Formal tool
Inventory of variables
Causal inference
Apr-17
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 C E D
Apr-17
H.S.

4. Example Exposure Disease Covariates Pysical Activity: PA
Diabetes type 2: D2
Covariates
Smoking: S
Health Conscious: HC
Overweight: Ov
Blood Pressure: BP
Apr-17
H.S.

5. Linear models Best model? Model choice can not be based on data only.
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.
All est significant (except PA=0)
20% D2 overall. PA from 0-5. Max PA is -10 pp.
Apr-17
H.S.

6. No influence of C E D C E D C E D C
Apr-17
H.S.

7. Confounder: Smoking Should adjust for Smoking Stratify Regression S
Negative bias + -
biased
true PA D2 -3 -2
Should adjust for Smoking
Stratify
Regression
Apr-17
H.S.

8. Confounder 2 Adjust for Smoking or for Health Consciousness+ - HC S
Negative bias
biased
true PA D2 -3 -2
Adjust for Smoking or
for Health Consciousness
Assume all following models are adjusted for smoking
Problem: if effect from HC to D2 (via diet )
If we include both, the simple pos/neg bias calc will not work unless both pathways have the same sign
Could adjust for HC if measured, or for both Smoking and Diet.
DAGs will not give this info, a important shortcoming.
Apr-17
H.S.

9. Intermediate (in 2. path): Overweight+ -
Alt 1: Ignore Overweight
Total PA D2
Alt 2: Two models:
Direct c
Indirect b1*c
Total c2+ b1*c1 -2.0 Ov Ov c1
Assume all these model are adjusted for smoking
b1=-0.25, c1=2, b1*c1=-0.5 b1 c2 PA PA D2
Simply adjusting for Overweight is not OK!
Apr-17
H.S.

10. Select limping subjects
Collider idea
Two causes for limping
Hip arthritis
Limp
Knee injury
Select limping subjects +
Limp + +
Hip arthritis
Knee injury -
Conditioning on a collider induces an association between the causes
Condition = (restrict, stratify, adjust)
Bias direction?
Hip arthritis and knee injury are not associated
Hip arthritis and knee injury are rare events
Apr-17
H.S.

11. Collider: Blood PressureBP
Positive bias if we adjust + -
true
biased PA D2
Should not adjust for Blood Pressure
Problem if selection is connected to BP
Study of subjects with high BP, decide to analyze PA-D2 association
Or, based on invitation letter advertising BP-measurement, people with high BP select into study
Apr-17
H.S.

12. Best model (so far) Model 2 is best
Used extra info in graphs to decide
All est significant (except PA=0)
20% D2 overall. PA from 0-5. Max PA is -10 pp.
Apr-17
H.S.

13. Effect modifier: Sex Alt 3 : Ignore Sex Alt 1 : Two modelsPA D2
Alt 1 : Two models
Easy
No test for interaction
Inefficient (12 estimates)
p=number of covariates
Estimates=2(p+1) versus p+2
Alt 2: Model with interaction
Technical
Test for interaction
Efficient (7 estimates)
Apr-17
H.S.

14. Effect modifier: Sex Model with interaction term
Linear model
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)
-2.5
-1.5
Apr-17
H.S.

15. Examples
Apr-17
H.S.

16. Smoking and LRTI 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?
LRTI
Smoke
Educ - S
Smoking in pregnancy
Lower Respiratory Tract Infections
Education a confounder?
Strong selection on educ in data, effect?
Education is a confounder
Selection represents
partial adjustment
Apr-17
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
Apr-17
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
Height
Ethnic
Apr-17
H.S.

19. Models Model 1 Lung func Ethnic Model 2 Lung func Hemo Height
Hart rate
Model 3
Model 4
Lung func
Hemo
Height
Ethnic
Model 1: total effect of ethnic group on lung function
Model 2: adjusted effect of hemoglobin on lung function
Model 3: Add all covariates, if effect of ethnic group, then some physio variable is missing
Model 4: ethnic group as a effect modifier of hemoglobin on lung function
Apr-17
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
The 3 first situations can not be gleaned from the data
Apr-17
H.S.