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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 e ect modi cation a. Brief recap of e ect modi cation (EM) b. Linking EM in our studies to reality c. Types of interaction d. Causal interaction / EM 1. Su cient 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

5.1.2 counterfactual framework

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Page 1: 5.1.2 counterfactual framework

Outline1. 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 report4. Integrating causal concepts into your research

Page 2: 5.1.2 counterfactual framework

Identifying confounding using DAGsOutline1. Review 3 traditional criteria for identifying

confounding2. DAG criteria to identify confounding3. Stratification decisions using DAGs4. Traditional criteria vs. DAGs

Page 3: 5.1.2 counterfactual framework

Review: 3 criteria for confounding

1. The factor causes the outcome in the source population

SES

Smoking Cancer

Page 4: 5.1.2 counterfactual framework

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

Page 5: 5.1.2 counterfactual framework

Review: 3 criteria for confounding

1. The factor causes the outcome in the source population2. Factor must be associated with the exposure in the source

population3. Factor must not be caused by exposure or

disease SES

CancerSmoking

X X

Page 6: 5.1.2 counterfactual framework

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

Page 7: 5.1.2 counterfactual framework

• 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

Page 8: 5.1.2 counterfactual framework

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

Page 9: 5.1.2 counterfactual framework

Identifying confounding with DAGs 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

Page 10: 5.1.2 counterfactual framework

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?

Page 11: 5.1.2 counterfactual framework

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

Page 12: 5.1.2 counterfactual framework

– 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

Page 13: 5.1.2 counterfactual framework

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

13Identifying confounding with DAGs Approach 1 - ‐

Example

Page 14: 5.1.2 counterfactual framework

– 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

Page 15: 5.1.2 counterfactual framework

– 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

Page 16: 5.1.2 counterfactual framework

– 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

Page 17: 5.1.2 counterfactual framework

– 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

Page 18: 5.1.2 counterfactual framework

Difficulty conceivingSES

Maternal genetics

Identifying confounding with DAGs

Vitamins Birth defects

18

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

Page 19: 5.1.2 counterfactual framework

– 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

Page 20: 5.1.2 counterfactual framework

20

1) No variables in C should be descendants of E or D2) Delete all non-ancestors of {E, D, C}3) Delete all arrows emanating from E4) Connect any two parents with a common child5) Strip arrowheads from all edges6) 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 DAGs 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

Page 21: 5.1.2 counterfactual framework

Identifying confounding with DAGs 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 YZ

A back- door ‐ path is present (blue arrows)

21

This is a directed path, and there are no back- ‐door pathways in this DAG

Page 22: 5.1.2 counterfactual framework

57

1. The potential confounders are not descendants of X2. 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 DAGs 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

Page 23: 5.1.2 counterfactual framework

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

Page 24: 5.1.2 counterfactual framework

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

Page 25: 5.1.2 counterfactual framework

• 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

Page 26: 5.1.2 counterfactual framework

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

Page 27: 5.1.2 counterfactual framework

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

Page 28: 5.1.2 counterfactual framework

28

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

Page 29: 5.1.2 counterfactual framework

29

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

Page 30: 5.1.2 counterfactual framework

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

Page 31: 5.1.2 counterfactual framework

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

Page 32: 5.1.2 counterfactual framework

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 WX ! W ! Y

1. There is one directed path from X to Y:2. W is a collider on that path

Rothman ME3, Pg 188, 195

Page 33: 5.1.2 counterfactual framework

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

Page 34: 5.1.2 counterfactual framework

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

Page 35: 5.1.2 counterfactual framework

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

Same variables different DAG ! W is a confounder under both criteria

Rothman ME3, Pg 188, 195