5.1.3 hills criteria

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



2. Factor must be associated with the exposure in the source population

SES

Smoking Cancer



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

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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

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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

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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

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Prenatal care

Difficulty conceivingSES

Maternal genetics

Identifying confounding with DAGs

Vitamins Birth defects

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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



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– 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





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Prenatal care


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


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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


Maternal genetics



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– 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


Maternal genetics


Vitamins Birth defects50


– 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


Maternal genetics



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– Test: are vitamins and birth defects still connected?– Yes – adjusting for prenatal care is not sufficient to control

confounding


Maternal genetics



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Maternal genetics



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– 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


Maternal genetics



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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


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

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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


• 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


Maternal genetics

• Controlling for prenatal care opens a path from SES to difficulty

conceiving



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• 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




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• 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

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• 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


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• 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 W1. W causes Y2. W causes X3. 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 ! Y1. 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


5.1.3 hills criteria

Education

Transcript of 5.1.3 hills criteria