Outline
1. What does causal inference entail?2. Using directed acyclic graphs
a. DAG basicsb. Identifying confoundingc. Understanding selection bias
3. Causal perspective on effect modificationa. Brief recap of effect modification (EM)b. Linking EM in our studies to realityc. Types of interactiond. Causal interaction / EM
1. Sufficient cause model (“causal pies”)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
Review: 3 criteria for confounding
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
Review: 3 criteria for confounding
1. The factor causes the outcome in the source population
2. Factor must be associated with the exposure in the sourcepopulation
3. Factor must not be caused by exposure or
diseaseSES
CancerSmoking
X X
Smoking
Smoking
CancerTar 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 DAGsApproach 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
Identifying confounding with DAGsApproach 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 conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
10
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
Identifying confounding with DAGs
Vitamins Birth defects
11
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-‐ancestors of 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
SES Difficulty conceiving
Prenatal care Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
12
Approach 1 -‐ Example
Prenatal care
Difficulty conceivingSES
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
Vitamins Birth defects
13
Identifying confounding with DAGsApproach 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
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
14
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
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects50
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
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
16
Approach 1 -‐ Example
– Test: are vitamins and birth defects still connected?– Yes – adjusting for prenatal care is not sufficient to control
confounding
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
17
Approach 1 -‐ Example
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
18
Approach 1 -‐ Example
– After adjusting for prenatal care, vitamins and birth defectswill still be associated even if vitamins have no causal effecton birth defects
– What set would be sufficient to control confounding?– Prenatal care and one of SES, difficulty conceiving or maternal
genetics
Difficulty conceivingSES
Maternal genetics
Identifying confounding with DAGs
Vitamins Birth defects
19
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
Identifying confounding with DAGsApproach 1 – Summary of Steps
• Summary of steps to assess whether adjustment for a setof confounders “C” sufficient to control for confounding ofthe relationship between E and D
Identifying confounding with DAGsApproach 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 YZ
A back-‐door path 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
Identifying confounding with DAGsApproach 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
Difficulty conceivingSES
Maternal genetics
• Controlling for prenatal care opens a path from SES to difficulty
conceiving
Identifying confounding with DAGs
Vitamins Birth defects
23
Approach 2 -‐ Example
Prenatal care Maternal genetics
• 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
SES Difficulty conceiving
Identifying confounding with DAGs
Vitamins Birth defects
24
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
26
• 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
Identifying confounding with DAGs
27
• 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
Identifying confounding with DAGs
2
8
Identifying confounding with DAGs
• 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
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
3 traditional criteria ! We should control for W1. W causes Y2. W causes X3. W is not affected by X or Y
Rothman ME3, Pg 188, 195
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
DAG criteria ! We should not control for W
X ! W ! Y1. There is one directed path from X to Y:
2. W is a collider on that path
Rothman ME3, Pg 188, 195
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
Conditioning on W could lead to unintentional collider bias!
Rothman ME3, Pg 188, 195
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
What are alternative sets of variables we could control for using DAG criteria?
Rothman ME3, Pg 188, 195