5.1.2 counterfactual framework

1. 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

2. 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

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

4. 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

5. 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 3. Factor must not be caused by exposure or disease SES CancerSmoking X X

6. 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

7. • 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

8. 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

9. 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

10. Prenatal care Difficulty conceivingSES Maternal genetics Identifying confounding with DAGs 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?

11. Prenatal care Maternal genetics Identifying confounding with DAGs Vitamins Birth defects 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

12. – 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 SES Difficulty conceiving Prenatal care Maternal genetics Identifying confounding with DAGs Vitamins Birth defects 1 2 Approach 1 -‐Example

13. 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 1 3 Identifying confounding with DAGs Approach 1 -‐Example

14. – 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 1 4 Approach 1 -‐Example

15. – 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 defects 50 Approach 1 -‐Example

16. – 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 1 6 Approach 1 -‐Example

17. – 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 1 7 Approach 1 -‐Example

18. Difficulty conceivingSES Maternal genetics Identifying confounding with DAGs Vitamins Birth defects 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

19. – 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 1 9 Approach 1 -‐Example

20. 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 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

21. 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-‐doorpath is present (blue arrows) 2 1 This is a directed path, and there are no back-‐ door pathways in this DAG

22. 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 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

23. 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 2 3 Approach 2 -‐Example

24. 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 2 4 Approach 2 -‐Example

25. • 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. 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 Identifying confounding with DAGs

27. 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 Identifying confounding with DAGs

28. 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

29. 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

30. 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

31. 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 W 1. W causes Y 2. W causes X 3. W is not aﬀected by X or Y Rothman ME3, Pg 188, 195

32. 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

33. 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

34. 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

35. 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

5.1.2 counterfactual framework

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5.1.2 counterfactual framework