5.2.2 dags for confounding

Outline
1. What does causal inference entail?
2. Using directed acyclic graphs
a. DAG basics
b. Identifying confounding
c. Understanding selection bias
3. Causal perspective on effect modification
a. Brief recap of effect modification (EM)
b. Linking EM in our studies to reality
c. Types of interaction
d. Causal interaction / EM
1. Sufficient cause model (“causalpies”)
2. Potential outcomes model (“causal types”)
e. Choosing which measure of interaction to estimate and report
4. Integrating causal concepts into your research

Identifying confounding using DAGs
Outline
1. Review 3 traditional criteria for identifying
confounding
2. DAG criteria to identify confounding
3. Stratiﬁcation decisions using DAGs
4. Traditional criteria vs. DAGs

Review: 3 criteria for confounding
1. The factor causes the outcome in the source
population
SES
Smoking Cancer

1. The factor causes the outcome in the source
population
2. Factor must be associated with the exposure
in the source population
SES
Smoking Cancer

1. The factor causes the outcome in the source population
2. Factor must be associated with the exposure in the source
population
3. Factor must not be caused by exposure or
disease SES
Cancer
Smoking
X X

Smoking
Smoking
Cancer
T
ar Mutations
Cancer
• Absence of a directed path from X to Y
implies X has no eﬀect on Y
– Directed paths not in the graph as important as those in
the graph
• Note: Not all intermediate steps between two
variables need to be represented
– Depends on level of detail of the model
6
Quick DAG assumptions reminder

• All common causes of exposure and disease are
included
– Common causes that are not observed should still be
included
U (religious
beliefs, culture,
lifestyle, etc.)
Alcohol Use
Smoking
Heart Disease
Quick DAG assumptions reminder
7

Identifying confounding with DAGs
Approach 1
1) Remove all direct effects of the exposure
– These are the effects of interest
– In their absence, is an association still present?
– This can be assessed with the next step
Health behaviors
Vitamins Cancer
8

Approach 1
2) Check whether disease and exposure share a common
cause (ancestor)
– Does any variable connect to E and to D by following only
forward pointing arrows?
– If E and D have a common cause then confounding is present
– A common cause will lead to an association between E and D
that is not due to the effect of E on D
Health behaviors
Vitamins Cancer
9

Prenatal care
Difficulty conceiving
SES
Maternal genetics
Vitamins Birth defects
1
0
Approach 1 -
‐Example
– If we just adjust for prenatal care, is it suﬃcient to control
for confounding between vitamins and birth defects?

Prenatal care Maternal genetics
1
1
Approach 1 -
‐Example
– Step 1: Is prenatal care caused by vitamin use or birth
defects? If yes, we should not adjust for it
– Do not adjust for an eﬀect of the exposure or outcome of
interest
SES Difficulty conceiving

– Step 2: Delete all non-‐ancestorsof vitamin use, birth
defects, or prenatal care
– If not an ancestor of vitamin use or birth defects, then cannot be a
common cause
– If not an ancestor of prenatal care, then new associations between
exposure and disease cannot be created by adjusting for prenatal
care
1
2
Approach 1 -
‐Example

Prenatal care
SES
Maternal genetics
– Step 3: Delete all direct eﬀects of vitamins
– These are the eﬀects of interest
– In their absence, is an association still present?
– If so, we still have confounding
1
3
Approach 1 -
‐Example

– Step 4: Connect any two causes sharing a common eﬀect
– Adjustment for the eﬀect will result in association of its common
causes
Prenatal care
SES
Maternal genetics
1
4
Approach 1 -
‐Example

– Step 5 : Strip arrow heads from all edges
– Moving from a graph that represents causal eﬀects to a graph that
represents the associations we expect to observe under null
hypothesis (as a result of both confounding and adjustment)
Prenatal care
SES
Maternal genetics
50
Approach 1 -
‐Example

– Step 6 : Delete prenatal care
– Equivalent to adjusting for prenatal care, now that we have added
to the graph the new associations that will be created by adjusting
Prenatal care
SES
Maternal genetics
1
6
Approach 1 -
‐Example

– Test: are vitamins and birth defects still connected?
– Yes – adjusting for prenatal care is not suﬃcient to control
confounding
SES
Maternal genetics
1
7
Approach 1 -
‐Example

SES
Maternal genetics
1
8
Approach 1 -
‐Example
– After adjusting for prenatal care, vitamins and birth defects
will still be associated even if vitamins have no causal eﬀect
on birth defects

– What set would be suﬃcient to control confounding?
– Prenatal care and one of SES, diﬃculty conceiving or maternal
genetics
SES
Maternal genetics
1
9
Approach 1 -
‐Example

2
0
1) No variables in C should be descendants of E or D
2) Delete all non-ancestors of {E, D, C}
3) Delete all arrows emanating from E
4) Connect any two parents with a common child
5) Strip arrowheads from all edges
6) Delete C
• Test: If E is disconnected from D in the remaining graph,
then adjustment for C is sufficient to remove confounding
Approach 1 – Summary of Steps
• Summary of steps to assess whether adjustment for a set
of confounders “C” sufficient to control for confounding of
the relationship between E and D

Approach 2
X Y
• Goal: block all back-door paths from X to Y
• Back-door path: an undirected path from X to Y that has an arrow
pointing into X
Z
X Y
Z
A back-‐doorpath is
present (blue arrows)
2
1
This is a directed path,
and there are no back-‐
door pathways in this
DAG

57
1. The potential confounders are not descendants of X
2. There is no open back-door path from X to Y after controlling for them
• When the back-door criterion is met, we can identify the effect of X
on Y
Approach 2
• Back-door criterion:
X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk

Prenatal care
SES
Maternal genetics
• Controlling for prenatal care opens a path from SES to difficulty
conceiving
2
3
Approach 2 -
‐Example

• Controlling for prenatal care opens a path from SES to difficulty
conceiving
• Controlling for maternal genetics or difficulty conceiving closes the
remaining backdoor pathway
• To identify the effect of vitamins on birth defects, control for prenatal
care & maternal genetics or prenatal care & difficulty conceiving
2
4
Approach 2 -
‐Example

• Criterion 2 states the confounder is “associated with the
exposure in the source population”
• For association to exist when one variable does not
cause the other, they have to share a common cause –
the common cause may be unmeasured
U (religious
beliefs, culture,
lifestyle, etc.)
Alcohol Use
Smoking Heart Disease
Note on a connection between DAG
and 3 criteria approaches
60

2
6
• Lessons learned
• It may not be immediately intuitive what variables we
need to control for in our analysis
• Adjustment/stratiﬁcation can introduce new sources of
association in our data
• These must be accounted for in our attempt to control
confounding
• Step by step analysis of a DAG provides a rigorous check
whether we have adequately controlled for confounding

2
7
• Lessons learned
• Adjustment for several different sets of confounders may
each be sufficient to control confounding of the same
exposure disease relation
• Can inform study design
• Example: may be easier to measure SES than difficulty
conceiving or genetics

2
8
• Objection to identifying confounding using causal
relations:
– Knowledge of my problem is too limited to specify a DAG
• Response:
– Problem is inherent in your analysis – not fault of the
DAG!
• Treating a variable as a confounder makes
assumptions about causal relations, whether you
have depicted them or not
• DAGs can help you recognize the assumptions you
are making

2
9
3 Traditional criteria vs. DAGs
– What does this provide that the “three rules”
approach does not?
– Clear identiﬁcation of colliders
– Suﬃciency of confounder adjustment
– Usually the “three rules” approach and the DAG
approach agree, but when they do not it is the “three
rules” that fail

Example of disagreement between 3 criteria and DAGs
X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
• Is mother’s diabetes history a confounder of the relationship
between low education and diabetes?
Rothman ME3, Pg 188, 195

X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
3 traditional criteria ! We should control for W
1. W causes Y
2. W causes X
3. W is not aﬀected by X or Y

X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
DAG criteria ! We should not control for W
X ! W ! Y
1. There is one directed path from X to Y:
2. W is a collider on that path

X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
Conditioning on W could lead to unintentional collider bias!

X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
What are alternative sets of variables we could control for using DAG criteria?

X: Low
education
Y: Diabetes
W: Mother
had diabetes
Z1: Family
income
during
childhood
Z2 :Mother’s
genetic
diabetes risk
Same variables diﬀerent DAG ! W is a confounder under both criteria

5.2.2 dags for confounding

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5.2.2 dags for confounding