1. DAGs intro with exercises 3h DirectedAcyclicGraph
Åpne «DAGs intro…, Answers» samtidig
I KES:
09:00 09:45 1 DAGs
10:00 10:45 1 DAGs
11:00 11:45 1 DAGs
11:45 12:30 1 Lunch
12:30 13:15 1 Measures
13:30 14:15 1 Design
14:30 15:15 1 Design
15:30 16: Design
Hein Stigum
courses
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 1 1 1 1 1

2. Agenda Background DAG concepts Analyzing DAGs More on DAGs Exercises
Association, Cause
Confounder, Collider, Mediator
Causal thinking
Paths
Analyzing DAGs
Examples
More on DAGs
Exercises
DAG concepts
Define a few main concepts
Paths: Surprisingly few rules needed
Analyzing DAGs
Examples: conf, intermediate, collider
Selection bias, Information bias
Rand, Mend Rand
The two former: manual for use
More on DAGs
Deeper thoughts and problems
With exercises, difficult to guess time
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 2 2 2 2 2

3. Why causal graphs? Estimate effect of exposure on disease Problem
Association measures are biased
Causal graphs help:
Understanding
Confounding, mediation, selection bias
Analysis
Adjust or not
Discussion
Precise statement of prior assumptions
Weight and blood pressure
Smoking and cancer
Tox and birth weight
Nov-18
H.S.

4. Causal versus casual
CONCEPTS
Nov-18
H.S.

5. Precision and validity
Measures of populations
precision - random error
validity - systematic error
True
value
Estimate
Precision
Bias
Ignore errors at individual level
measure pop, measure sample
aim: measure as precisely and as correctly as possible
DAGs only consider bias
11/17/2018
H.S.

6. DAG=Directed Acyclic Graph
god-DAG
Causal Graph:
Node = variable
Arrow = cause
E=exposure, D=disease
DAG=Directed Acyclic Graph
Read of the DAG:
Causality = arrows
Associations = paths
Independencies = no paths
Estimations:
E-D association has two parts:
ED causal effect keep open
ECUD bias try to close
Arrows=lead to or causes
Time
E- exposure
D- disease
C, V - cofactor, variable
U- unmeasured
Directed= arrows
Acyclic = nothing can cause itself
E[C]UD Condition (adjust) to close
Time 
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 6 6 6

7. Association and Cause Association 3 possible causal structure E D
(Reversed cause) E D
Assume E precedes D in time
Association: observe
Cause: infer (extra knowledge)
Causal structure force on the data
Basic structures, may generalize with many more variables: use paths
+ more complicated structures
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 7 7 7

8. Confounder idea + A common cause Adjust for smoking Smoking
Yellow fingers
Smoking
Lung cancer + + +
Yellow fingers
Lung cancer +
A confounder induces an association between its effects
Conditioning on a confounder removes the association
Condition = (restrict, stratify, adjust)
Paths
Simplest form
Causal confounding, may have non-causal confounding
“+” (assume monotonic effects)
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S. 8 8 8 8 8

9. Two causes for selection to study
Collider idea
Two causes for selection to study
Selected subjects
Selected
Yellow fingers
Selected
Lung cancer + + +
Yellow fingers
Lung cancer or
+ and
Conditioning on a collider induces an association between its causes
“And” and “or” selection leads to different bias
Paths
Simplest form
“+” (assume monotonic effects)
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S. 9 9 9 9 9

10. Mediator Have found a cause (E) How does it work? Mediator (M) M E D
indirect
effect
How does it work?
Mediator (M)
Paths E
direct effect D
𝑇𝑜𝑡𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡=𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡+𝑑𝑖𝑟𝑒𝑐𝑡
𝑀𝑒𝑑𝑖𝑎𝑡𝑒𝑑 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛= 𝑖𝑛𝑑𝑖𝑟𝑒𝑐𝑡 𝑡𝑜𝑡𝑎𝑙
Could be Statin->Cholesterol->CHD
Or exercise->BMI->CVD
Use ordinary regression methods if:
linear model and
no E-M interaction.
Otherwise, need new methods
Nov-18
H.S.

11. Causal thinking in analyses
Nov-18
H.S.

12. Regression before DAGs
Risk factors for D:
Use statistical criteria for variable selection
Variable OR
Comments E
2.0 C
1.2
Surprisingly low association
Report all variables in the model as equals
Association
Both can be misleading! C E D
Nov-18
H.S.

13. Statistical criteria for variable selection
- Want the effect of E on D (E precedes D)
- Observe the two associations C-E and C-D
- Assume statistical criteria dictates adjusting for C
(likelihood ratio, Akaike (赤池 弘次) or 10% change in estimate) C E D
The undirected graph above is compatible with three DAGs: C C C E D E D E D
Confounder
1. Adjust
Mediator
2. Direct: adjust
3. Total: not adjust
Collider
4. Not adjust
Hirotugu Akaike 赤池 弘次
Conclusion: The data driven method is correct in 2 out of 4 situations
Need information from outside the data to do a proper analysis
DAGs variable selection: close all non-causal paths
Nov-18
H.S.

14. Association versus causation
Risk factors for D:
Use statistical criteria for variable selection
Variable OR
Comments E
2.0 C
1.2
Surprisingly low association
Report all variables in the model as equals
Association
Causation
Base adjustments
on a DAG C C
Could be Diabetes->Fractures with Exercise as confounder
Report only
the E-effect E D E D
Symmetrical
Directional
C is a confounder for E-D
E is a confounder for C-D
C is a confounder for ED
E is a mediator for CD
Nov-18
H.S.

15. Paths The Path of the Righteous Nov-18 Nov-18 Nov-18 H.S. H.S. H.S. 15
Ezekiel 25:17. "The Path of the Righteous Man Is Beset on All Sides by The inequities of the Selfish and the Tyranny of Evil Men."
(Pulp Fiction version)
Paths
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 15 15

16. Path definitions
Path: any trail from E to D (without repeating itself)
Type: causal, non-causal
State: open, closed
Path 1
E®D 2
E®M®D 3
E¬C®D 4
E®K¬D
Four paths:
Notice: path with or against the arrows
Paths show potential association
Goal:
Keep causal paths of interest open
Close all non-causal paths
Nov-18
Nov-18
H.S.
H.S. 16

17. Four rules 1. Causal path: ED 2. Closed path: K
(all arrows in the same direction) otherwise non-causal
Before conditioning:
2. Closed path: K
(closed at a collider, otherwise open)
Conditioning on:
3. a non-collider closes: [M] or [C]
4. a collider opens: [K]
(or a descendant of a collider)
Nov-18
H.S.

18. ANALYZING DAGs
Nov-18
H.S.

19. Confounding examples Nov-18 Nov-18 Nov-18 Nov-18 Nov-18 Nov-18 H.S.
Informal, no strict notation/def
Casual about the causal!
Confounding examples
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 19 19 19 19 19 19

20. Vitamin and birth defects
Is there a bias in the crude E-D effect?
Should we adjust for C?
What happens if age also has a direct effect on D?
Unconditional
Path
Type
Status 1
E®D
Causal
Open 2
E¬C®U®D
Non-causal
Bias
This is an example
of confounding
Noncausal open=biasing path
Both C and U are confounders
Problem that we have ”forgotten” arrow C->D?
Conditioning on C
Path
Type
Status 1
E®D
Causal
Open 2
E¬[C]®U®D
Non-causal
Closed
Question:
Is U a confounder?
No bias 3
E¬[C] ®D
Non-causal
Closed
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 20 20 20

21. Exercise: Physical activity and Coronary Heart Disease (CHD)
We want the total effect of Physical Activity on CHD.
Write down the paths.
Are they causal/non-causal, open/closed?
What should we adjust for?
Noncausal open=biasing path
5 minutes
Nov-18
Nov-18
Nov-18
H.S.
H.S. 21 21

22. Intermediate variables
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 22 22 22 22 22 22

23. Exercise: Tea and depression
Write down the paths. Show type and status.
You want the total effect of tea on depression. What would you adjust for?
You want the direct effect of tea on depression. What would you adjust for?
Is caffeine an intermediate variable or a confounder?
Tea and depression: Finnish study
Caffeine reduces depression: Nurses Health Study
10 minutes
Nov-18
H.S.

24. Exercise: Statin and CHD
Write down the paths. Show type and status.
You want the total effect of statin on CHD. What would you adjust for?
If lifestyle is unmeasured, can we estimate the direct effect of statin on CHD (not mediated through cholesterol)?
Is cholesterol an intermediate variable or a collider? C
cholesterol U
lifestyle E
statin D
CHD
Statin: lipid (cholesterol) lowering drug
10 minutes
Nov-18
H.S.
H.S. 24 24

25. Direct and indirect effects
So far: Controlled (in)direct effect
Causal interpretation: linear model and no E-M interaction
New concept: Natural (in)direct effect
Causal interpretation also for: non-linear model , E-M interaction
Controlled effect = Natural effect if
linear model and no E-M interaction
Hafeman and Schwartz 2009;
Lange and Hansen 2011;
Pearl 2012;
Robins and Greenland 1992;
VanderWeele 2009, 2014
Nov-18
H.S.

26. Mixed Confounder, collider and mediator Nov-18 Nov-18 Nov-18 Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 26 26 26 26 26 26

27. Diabetes and Fractures
We want the total effect of
Diabetes (type 2) on fractures
Conditional
Path
Type
Status 1
E→D
Causal
Open 2
E→F→D 3
E→B→D 4
E←[V]→B→D
Non-causal
Closed 5
E←[P]→B→D
Unconditional
Path
Type
Status 1
E→D
Causal
Open 2
E→F→D 3
E→B→D 4
E←V→B→D
Non-causal 5
E←P→B→D
Questions:
More paths?
B a collider?
V and P ind?
Diabetes->eye disease->fall,
could have ->eye disease->physical activity->
Diabetes II reduces bone density, BMI increases bone density
Questions: more paths (E-B-P-E-D)? Two (or three) arrows are colliding in B, is B a collider?
Mediators
Confounders
Nov-18
H.S.

28. Selection bias Nov-18 Nov-18 Nov-18 Nov-18 Nov-18 Nov-18 H.S. H.S.28 28 28 28 28 28

29. Convenience sample, homogenous sample
hospital
Convenience sample:
Conduct the study among
hospital patients? E
diabetes D
fractures
2. Homogeneous sample:
Population data,
exclude hospital patients?
Conditional
Path
Type
Status 1
E→D
Causal
Open 2
E→[H]←D
Non-Causal
Unconditional
Path
Type
Status 1
E→D
Causal
Open 2
E→H←D
Non-causal
Closed
Collider, selection bias
Collider stratification bias: at least on stratum is biased
This type of selection bias can be adjusted for!
Nov-18
H.S.

30. Adjusting for Selection bias
Paths
Type
Status
smoke®CHD
Causal
Open
smoke¬sex®[S]¬age®CHD
Non-causal
sex
age
smoke
CHD
Adjusting for sex or age or both
removes the selection bias
Common table of properties?
Both types of selection may operate in the named examples.
Ref to Pearl
Selection bias types:
Berkson’s, loss to follow up, nonresponse, self-selection, healthy worker
Hernan et al, A structural approach to selection bias, Epidemiology 2004
Nov-18
H.S.

31. Drawing DAGs with DAGitty
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 31 31 31 31 31 31

32. Drawing a causal DAG Start: E and D 1 exposure, 1 disease
add: [S] variables conditioned by design
add: C-s all common causes of 2 or more
variables in the DAG C
C must be included common cause
V may be excluded exogenous
M may be excluded mediator
K may be excluded unless we condition V E D M K
Nov-18
H.S.

33. DAGitty drawing tool DAGitty Web page Draw DAGs Find adjustment sets
Test DAGs
Web page
Run or download
DAGitty is developed and maintained by Johannes Textor, Theoretical Biology & Bioinformatics group, University of Utrecht
Nov-18 HS

34. Interface
Nov-18 HS

35. Draw model Draw new model New variables, connect
Model>New model, Exposure, Outcome
New variables, connect
n new variable (or double click)
c connect (hit c over V1 and over V2 to connect)
r rename
d delete
Status (toggle on/off)
u unobserved
a adjusted
Nov-18 HS

36. Export DAG Export to Word or PowerPoint
“Zoom” the DAGitty drawing first (Ctrl-roll)
Use “Snipping tool” or
use Model>Export as PDF
Without zooming
With zooming
Nov-18 HS

37. Randomized experiments
Difficult: present only if time for exercise
Randomized experiments
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S.
H.S.
H.S. 37 37 37 37 37 37

38. Strength of arrow C1 E D C2 C3 C R E D U R E D C1, C2, C3 exogenous
Not
deterministic E D C2
C1, C2, C3 exogenous
Adjust for C1, C2, C3? C3 C
full
compliance
Full compliance
 no E-D confounding R E D
deterministic U
Not full compliance
weak E-D confounding
but R-D is unconfounded
not full
compliance R E D
Path
Type
Status 1
R®E®D
Causal
open 2
R®E¬U®D
non-causal
closed
Sub analysis conditioning on E
may lead to bias
Nov-18
H.S.

39. Randomized experiments
Observational study
Randomized experiment with full compliance
R= randomized treatment
E= actual treatment.
R=E
Randomized experiment with less than full compliance (c) c
IVe
No way of drawing that R=E or that R has strong effect on E (R-E arrow is determinisric)
If R has strong effect on E then U must have weak effect, that is little confounding.
ITT weaker than IV effect, combination of behavior (compliance) and biology
Per Protocol=as treated
If linear model: ITTe=c*IVe, c<1
ITTe
IntentionToTreat effect: effect of R on D (unconfounded) population
PerProtocol: crude effect of E on D (confounded by U)
InstrumentalVariable effect: adjusted effect of E on D (if c is known, 2SLS) individual
Nov-18
H.S.

40. Exercise: RandomizedControlledTrial
Calculate the compliance (c) as a risk difference from the table.
Calculate the intention to treat effect (ITTe) as a risk difference.
Calculate the per-protocol effect (PP) as a risk difference.
Calculate the instrumental variable effect (IVe).
Explain the results in words. c
IVe
ITTe
10 minutes
Nov-18
H.S.

41. MORE ON DAGs
Nov-18
H.S.

42. Confounding versus selection bias
Path: Any trail from E to D (without repeating itself)
Open non-causal path = biasing path
Confounding and selection bias not always distinct
May use DAG to give distinct definitions: C E D B A
Confounding:
Non-causal path
without colliders C E D B A
Selection bias:
Non-causal path open
due to conditioning
on a collider E D B A
Causal
Note: interaction based selection bias not included
Hernan et al, A structural approach to selection bias, Epidemiology 2004
Nov-18
H.S.

43. Better discussion based on DAGs before your conclusions
Summing up
Data driven analyses do not work. Need (causal) information from outside the data.
DAGs are intuitive and accurate tools to display that information.
Paths show the flow of causality and of bias and guide the analysis.
DAGs clarify concepts like confounding and selection bias, and show that we can adjust for both.
Better discussion based on DAGs
Draw your assumptions
before your conclusions
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 43 43

44. Recommended reading Books Papers
Hernan, M. A. and J. Robins. Causal Inference. Web:
Rothman, K. J., S. Greenland, and T. L. Lash. Modern Epidemiology, 2008.
Morgan and Winship, Counterfactuals and Causal Inference, 2009
Pearl J, Causality – Models, Reasoning and Inference, 2009
Veierød, M.B., Lydersen, S. Laake,P. Medical Statistics. 2012
Papers
Greenland, S., J. Pearl, and J. M. Robins. Causal diagrams for epidemiologic research, Epidemiology 1999
Hernandez-Diaz, S., E. F. Schisterman, and M. A. Hernan. The birth weight "paradox" uncovered? Am J Epidemiol 2006
Hernan, M. A., S. Hernandez-Diaz, and J. M. Robins. A structural approach to selection bias, Epidemiology 2004
Berk, R.A. An introduction to selection bias in sociological data, Am Soc R 1983
Greenland, S. and B. Brumback. An overview of relations among causal modeling methods, Int J Epidemiol 2002
Weinberg, C. R. Can DAGs clarify effect modification? Epidemiology 2007
Hernan and Robins Causal inference (web)
Hernan a struct approach
Hernandez- From causal
Shahar
Rothman
Nov-18
Nov-18
Nov-18
Nov-18
H.S.
H.S.
H.S. 44 44 44